LMFDB - Embedded newform 525.2.t.h.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(26,525)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("525.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 8 x^{18} - 15 x^{17} + 18 x^{16} - 45 x^{15} + 59 x^{14} - 147 x^{13} + 271 x^{12} + \cdots + 59049 $ x^20 - 3x^19 + 8x^18 - 15x^17 + 18x^16 - 45x^15 + 59x^14 - 147x^13 + 271x^12 - 330x^11 + 879x^10 - 990x^9 + 2439x^8 - 3969x^7 + 4779x^6 - 10935x^5 + 13122x^4 - 32805x^3 + 52488x^2 - 59049*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.4
Root			$1.71408 - 0.248842i$ of defining polynomial
Character	$\chi$	$=$	525.101
Dual form			525.2.t.h.26.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.780577 + 0.450666i) q^{2} +(-1.71408 + 0.248842i) q^{3} +(-0.593800 + 1.02849i) q^{4} +(1.22583 - 0.966719i) q^{6} +(0.105498 + 2.64365i) q^{7} -2.87309i q^{8} +(2.87616 - 0.853070i) q^{9} +O(q^{10})$	\(q+(-0.780577 + 0.450666i) q^{2} +(-1.71408 + 0.248842i) q^{3} +(-0.593800 + 1.02849i) q^{4} +(1.22583 - 0.966719i) q^{6} +(0.105498 + 2.64365i) q^{7} -2.87309i q^{8} +(2.87616 - 0.853070i) q^{9} +(5.46176 + 3.15335i) q^{11} +(0.761890 - 1.91068i) q^{12} +3.77183i q^{13} +(-1.27375 - 2.01603i) q^{14} +(0.107205 + 0.185685i) q^{16} +(1.88963 - 3.27294i) q^{17} +(-1.86061 + 1.96207i) q^{18} +(-4.57893 + 2.64365i) q^{19} +(-0.838682 - 4.50518i) q^{21} -5.68443 q^{22} +(-5.87050 + 3.38933i) q^{23} +(0.714944 + 4.92471i) q^{24} +(-1.69984 - 2.94420i) q^{26} +(-4.71769 + 2.17794i) q^{27} +(-2.78161 - 1.46129i) q^{28} -3.06327i q^{29} +(0.349819 + 0.201968i) q^{31} +(4.80897 + 2.77646i) q^{32} +(-10.1466 - 4.04598i) q^{33} +3.40637i q^{34} +(-0.830485 + 3.46465i) q^{36} +(-0.668021 - 1.15705i) q^{37} +(2.38281 - 4.12714i) q^{38} +(-0.938588 - 6.46523i) q^{39} -6.53749 q^{41} +(2.68499 + 3.13867i) q^{42} +4.84564 q^{43} +(-6.48638 + 3.74491i) q^{44} +(3.05492 - 5.29127i) q^{46} +(-0.970371 - 1.68073i) q^{47} +(-0.229964 - 0.291602i) q^{48} +(-6.97774 + 0.557800i) q^{49} +(-2.42454 + 6.08030i) q^{51} +(-3.87929 - 2.23971i) q^{52} +(1.24774 + 0.720381i) q^{53} +(2.70100 - 3.82615i) q^{54} +(7.59543 - 0.303106i) q^{56} +(7.19082 - 5.67086i) q^{57} +(1.38051 + 2.39112i) q^{58} +(-1.60223 + 2.77514i) q^{59} +(-11.3644 + 6.56124i) q^{61} -0.364081 q^{62} +(2.55864 + 7.51354i) q^{63} -5.43385 q^{64} +(9.74358 - 1.41452i) q^{66} +(-1.55082 + 2.68611i) q^{67} +(2.24412 + 3.88694i) q^{68} +(9.21911 - 7.27042i) q^{69} +2.21562i q^{71} +(-2.45094 - 8.26345i) q^{72} +(2.18121 + 1.25932i) q^{73} +(1.04288 + 0.602109i) q^{74} -6.27919i q^{76} +(-7.76013 + 14.7716i) q^{77} +(3.64630 + 4.62362i) q^{78} +(-3.05960 - 5.29938i) q^{79} +(7.54454 - 4.90712i) q^{81} +(5.10301 - 2.94623i) q^{82} +8.53654 q^{83} +(5.13154 + 1.81259i) q^{84} +(-3.78240 + 2.18377i) q^{86} +(0.762268 + 5.25069i) q^{87} +(9.05984 - 15.6921i) q^{88} +(-0.590783 - 1.02327i) q^{89} +(-9.97138 + 0.397921i) q^{91} -8.05034i q^{92} +(-0.649878 - 0.259141i) q^{93} +(1.51490 + 0.874627i) q^{94} +(-8.93387 - 3.56241i) q^{96} +9.10556i q^{97} +(5.19528 - 3.58004i) q^{98} +(18.3989 + 4.41026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{3} + 14 q^{4} - 7 q^{9}+O(q^{10}) $ 20 * q - 3 * q^3 + 14 * q^4 - 7 * q^9	$ 20 q - 3 q^{3} + 14 q^{4} - 7 q^{9} + 21 q^{12} - 18 q^{16} - 14 q^{18} - 9 q^{21} - 20 q^{22} + 18 q^{24} + 10 q^{28} + 42 q^{31} - 12 q^{33} - 36 q^{36} - 24 q^{37} - 33 q^{42} - 36 q^{43} - 8 q^{46} - 4 q^{49} + 21 q^{51} + 84 q^{52} - 75 q^{54} - 6 q^{57} + 4 q^{58} - 90 q^{61} + 5 q^{63} - 120 q^{64} + 6 q^{66} - 20 q^{67} + 35 q^{72} + 48 q^{73} + 108 q^{78} + 46 q^{79} + 29 q^{81} - 36 q^{82} + 75 q^{84} - 69 q^{87} - 4 q^{88} - 30 q^{91} + 30 q^{93} + 6 q^{94} + 135 q^{96} + 94 q^{99}+O(q^{100}) $ 20 * q - 3 * q^3 + 14 * q^4 - 7 * q^9 + 21 * q^12 - 18 * q^16 - 14 * q^18 - 9 * q^21 - 20 * q^22 + 18 * q^24 + 10 * q^28 + 42 * q^31 - 12 * q^33 - 36 * q^36 - 24 * q^37 - 33 * q^42 - 36 * q^43 - 8 * q^46 - 4 * q^49 + 21 * q^51 + 84 * q^52 - 75 * q^54 - 6 * q^57 + 4 * q^58 - 90 * q^61 + 5 * q^63 - 120 * q^64 + 6 * q^66 - 20 * q^67 + 35 * q^72 + 48 * q^73 + 108 * q^78 + 46 * q^79 + 29 * q^81 - 36 * q^82 + 75 * q^84 - 69 * q^87 - 4 * q^88 - 30 * q^91 + 30 * q^93 + 6 * q^94 + 135 * q^96 + 94 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.780577	+	0.450666i	−0.551951	+	0.318669i	−0.749909	−	0.661541i	$-0.769903\pi$
$2$	−0.780577	+	0.450666i	−0.551951	+	0.318669i	0.197957	+	0.980211i	$0.436569\pi$
$3$	−1.71408	+	0.248842i	−0.989626	+	0.143669i
$3$	−1.71408	+	0.248842i	−0.989626	+	0.143669i
$4$	−0.593800	+	1.02849i	−0.296900	+	0.514245i
$5$		0			0
$5$		0			0
$6$	1.22583	−	0.966719i	0.500443	−	0.394662i
$7$	0.105498	+	2.64365i	0.0398746	+	0.999205i
$7$	0.105498	+	2.64365i	0.0398746	+	0.999205i
$8$		−	2.87309i		−	1.01579i
$9$	2.87616	−	0.853070i	0.958719	−	0.284357i
$10$		0			0
$11$	5.46176	+	3.15335i	1.64678	+	0.950770i	0.978340	+	0.207005i	$0.0663717\pi$
$11$	5.46176	+	3.15335i	1.64678	+	0.950770i	0.668442	+	0.743765i	$0.266962\pi$
$12$	0.761890	−	1.91068i	0.219939	−	0.551566i
$13$			3.77183i			1.04612i	0.852297	+	0.523059i	$0.175209\pi$
$13$			3.77183i			1.04612i	−0.852297	+	0.523059i	$0.824791\pi$
$14$	−1.27375	−	2.01603i	−0.340425	−	0.538806i
$15$		0			0
$16$	0.107205	+	0.185685i	0.0268013	+	0.0464212i
$17$	1.88963	−	3.27294i	0.458303	−	0.793804i	−0.540569	−	0.841300i	$-0.681791\pi$
$17$	1.88963	−	3.27294i	0.458303	−	0.793804i	0.998871	+	0.0474963i	$0.0151242\pi$
$18$	−1.86061	+	1.96207i	−0.438550	+	0.462465i
$19$	−4.57893	+	2.64365i	−1.05048	+	0.606494i	−0.922783	−	0.385319i	$-0.874091\pi$
$19$	−4.57893	+	2.64365i	−1.05048	+	0.606494i	−0.127695	+	0.991813i	$0.540758\pi$
$20$		0			0
$21$	−0.838682	−	4.50518i	−0.183015	−	0.983110i
$22$	−5.68443			−1.21192
$23$	−5.87050	+	3.38933i	−1.22408	+	0.706725i	−0.965786	−	0.259340i	$-0.916495\pi$
$23$	−5.87050	+	3.38933i	−1.22408	+	0.706725i	−0.258298	+	0.966065i	$0.583162\pi$
$24$	0.714944	+	4.92471i	0.145937	+	1.00525i
$25$		0			0
$26$	−1.69984	−	2.94420i	−0.333365	−	0.577406i
$27$	−4.71769	+	2.17794i	−0.907920	+	0.419144i
$28$	−2.78161	−	1.46129i	−0.525675	−	0.276158i
$29$		−	3.06327i		−	0.568834i	−0.958701	−	0.284417i	$-0.908200\pi$
$29$		−	3.06327i		−	0.568834i	0.958701	−	0.284417i	$-0.0918000\pi$
$30$		0			0
$31$	0.349819	+	0.201968i	0.0628294	+	0.0362746i	0.531086	−	0.847318i	$-0.321784\pi$
$31$	0.349819	+	0.201968i	0.0628294	+	0.0362746i	−0.468256	+	0.883593i	$0.655118\pi$
$32$	4.80897	+	2.77646i	0.850114	+	0.490813i
$33$	−10.1466	−	4.04598i	−1.76629	−	0.704315i
$34$			3.40637i			0.584188i
$35$		0			0
$36$	−0.830485	+	3.46465i	−0.138414	+	0.577442i
$37$	−0.668021	−	1.15705i	−0.109822	−	0.190217i	0.805876	−	0.592084i	$-0.201695\pi$
$37$	−0.668021	−	1.15705i	−0.109822	−	0.190217i	−0.915698	+	0.401867i	$0.868361\pi$
$38$	2.38281	−	4.12714i	0.386542	−	0.669511i
$39$	−0.938588	−	6.46523i	−0.150294	−	1.03526i
$40$		0			0
$41$	−6.53749			−1.02098			−0.510492	−	0.859882i	$-0.670537\pi$
$41$	−6.53749			−1.02098			−0.510492	+	0.859882i	$0.670537\pi$
$42$	2.68499	+	3.13867i	0.414303	+	0.484308i
$43$	4.84564			0.738954			0.369477	−	0.929240i	$-0.379537\pi$
$43$	4.84564			0.738954			0.369477	+	0.929240i	$0.379537\pi$
$44$	−6.48638	+	3.74491i	−0.977858	+	0.564567i
$45$		0			0
$46$	3.05492	−	5.29127i	0.450423	−	0.780156i
$47$	−0.970371	−	1.68073i	−0.141543	−	0.245160i	0.786535	−	0.617546i	$-0.211873\pi$
$47$	−0.970371	−	1.68073i	−0.141543	−	0.245160i	−0.928078	+	0.372386i	$0.878540\pi$
$48$	−0.229964	−	0.291602i	−0.0331925	−	0.0420891i
$49$	−6.97774	+	0.557800i	−0.996820	+	0.0796858i
$50$		0			0
$51$	−2.42454	+	6.08030i	−0.339503	+	0.851412i
$52$	−3.87929	−	2.23971i	−0.537961	−	0.310592i
$53$	1.24774	+	0.720381i	0.171390	+	0.0989519i	0.583241	−	0.812299i	$-0.301784\pi$
$53$	1.24774	+	0.720381i	0.171390	+	0.0989519i	−0.411851	+	0.911251i	$0.635118\pi$
$54$	2.70100	−	3.82615i	0.367559	−	0.520673i
$55$		0			0
$56$	7.59543	−	0.303106i	1.01498	−	0.0405042i
$57$	7.19082	−	5.67086i	0.952447	−	0.751123i
$58$	1.38051	+	2.39112i	0.181270	+	0.313969i
$59$	−1.60223	+	2.77514i	−0.208592	+	0.361293i	−0.951271	−	0.308355i	$-0.900222\pi$
$59$	−1.60223	+	2.77514i	−0.208592	+	0.361293i	0.742679	+	0.669648i	$0.233555\pi$
$60$		0			0
$61$	−11.3644	+	6.56124i	−1.45506	+	0.840080i	−0.998762	−	0.0497461i	$-0.984159\pi$
$61$	−11.3644	+	6.56124i	−1.45506	+	0.840080i	−0.456300	+	0.889826i	$0.650825\pi$
$62$	−0.364081			−0.0462384
$63$	2.55864	+	7.51354i	0.322359	+	0.946618i
$64$	−5.43385			−0.679231
$65$		0			0
$66$	9.74358	−	1.41452i	1.19935	−	0.174116i
$67$	−1.55082	+	2.68611i	−0.189463	+	0.328160i	−0.945071	−	0.326864i	$-0.894008\pi$
$67$	−1.55082	+	2.68611i	−0.189463	+	0.328160i	0.755608	+	0.655024i	$0.227341\pi$
$68$	2.24412	+	3.88694i	0.272140	+	0.471360i
$69$	9.21911	−	7.27042i	1.10985	−	0.875256i
$70$		0			0
$71$			2.21562i			0.262946i	0.991320	+	0.131473i	$0.0419707\pi$
$71$			2.21562i			0.262946i	−0.991320	+	0.131473i	$0.958029\pi$
$72$	−2.45094	−	8.26345i	−0.288847	−	0.973857i
$73$	2.18121	+	1.25932i	0.255292	+	0.147393i	0.622185	−	0.782870i	$-0.286245\pi$
$73$	2.18121	+	1.25932i	0.255292	+	0.147393i	−0.366893	+	0.930263i	$0.619579\pi$
$74$	1.04288	+	0.602109i	0.121233	+	0.0699938i
$75$		0			0
$76$		−	6.27919i		−	0.720272i
$77$	−7.76013	+	14.7716i	−0.884349	+	1.68338i
$78$	3.64630	+	4.62362i	0.412862	+	0.523522i
$79$	−3.05960	−	5.29938i	−0.344232	−	0.596227i	0.640982	−	0.767556i	$-0.278527\pi$
$79$	−3.05960	−	5.29938i	−0.344232	−	0.596227i	−0.985214	+	0.171329i	$0.945194\pi$
$80$		0			0
$81$	7.54454	−	4.90712i	0.838283	−	0.545236i
$82$	5.10301	−	2.94623i	0.563534	−	0.325356i
$83$	8.53654			0.937007			0.468503	−	0.883462i	$-0.344793\pi$
$83$	8.53654			0.937007			0.468503	+	0.883462i	$0.344793\pi$
$84$	5.13154	+	1.81259i	0.559897	+	0.197770i
$85$		0			0
$86$	−3.78240	+	2.18377i	−0.407867	+	0.235482i
$87$	0.762268	+	5.25069i	0.0817237	+	0.562933i
$88$	9.05984	−	15.6921i	0.965782	−	1.67278i
$89$	−0.590783	−	1.02327i	−0.0626229	−	0.108466i	0.833014	−	0.553252i	$-0.186613\pi$
$89$	−0.590783	−	1.02327i	−0.0626229	−	0.108466i	−0.895637	+	0.444786i	$0.853280\pi$
$90$		0			0
$91$	−9.97138	+	0.397921i	−1.04529	+	0.0417135i
$92$		−	8.05034i		−	0.839306i
$93$	−0.649878	−	0.259141i	−0.0673892	−	0.0268716i
$94$	1.51490	+	0.874627i	0.156250	+	0.0902109i
$95$		0			0
$96$	−8.93387	−	3.56241i	−0.911809	−	0.363587i
$97$			9.10556i			0.924530i	0.886742	+	0.462265i	$0.152963\pi$
$97$			9.10556i			0.924530i	−0.886742	+	0.462265i	$0.847037\pi$
$98$	5.19528	−	3.58004i	0.524803	−	0.361639i
$99$	18.3989	+	4.41026i	1.84916	+	0.443247i
$100$		0			0
$101$	1.15241	−	1.99604i	0.114669	−	0.198613i	−0.802978	−	0.596008i	$-0.796753\pi$
$101$	1.15241	−	1.99604i	0.114669	−	0.198613i	0.917647	+	0.397395i	$0.130086\pi$
$102$	−0.847647	−	5.83880i	−0.0839296	−	0.578128i
$103$	6.74347	−	3.89335i	0.664454	−	0.383623i	−0.129518	−	0.991577i	$-0.541343\pi$
$103$	6.74347	−	3.89335i	0.664454	−	0.383623i	0.793972	+	0.607954i	$0.208010\pi$
$104$	10.8368			1.06264
$105$		0			0
$106$	−1.29861			−0.126132
$107$	4.72768	−	2.72952i	0.457042	−	0.263873i	−0.253758	−	0.967268i	$-0.581667\pi$
$107$	4.72768	−	2.72952i	0.457042	−	0.263873i	0.710800	+	0.703395i	$0.248333\pi$
$108$	0.561371	−	6.14536i	0.0540179	−	0.591337i
$109$	3.29331	−	5.70418i	0.315442	−	0.546362i	−0.664089	−	0.747653i	$-0.731181\pi$
$109$	3.29331	−	5.70418i	0.315442	−	0.546362i	0.979531	+	0.201292i	$0.0645139\pi$
$110$		0			0
$111$	1.43296	+	1.81704i	0.136011	+	0.172466i
$112$	−0.479575	+	0.303002i	−0.0453156	+	0.0286310i
$113$		−	0.214344i		−	0.0201638i	−0.999949	−	0.0100819i	$-0.996791\pi$
$113$		−	0.214344i		−	0.0201638i	0.999949	−	0.0100819i	$-0.00320922\pi$
$114$	−3.05732	+	7.66720i	−0.286344	+	0.718099i
$115$		0			0
$116$	3.15054	+	1.81897i	0.292520	+	0.168887i
$117$	3.21763	+	10.8484i	0.297470	+	1.00293i
$118$		−	2.88828i		−	0.265888i
$119$	8.85184	+	4.65023i	0.811447	+	0.426286i
$120$		0			0
$121$	14.3872	+	24.9193i	1.30793	+	2.26539i
$122$	5.91386	−	10.2431i	0.535415	−	0.927367i
$123$	11.2058	−	1.62680i	1.01039	−	0.146683i
$124$	−0.415445	+	0.239857i	−0.0373081	+	0.0215398i
$125$		0			0
$126$	−5.38332	−	4.71181i	−0.479584	−	0.419761i
$127$	−1.05320			−0.0934560			−0.0467280	−	0.998908i	$-0.514879\pi$
$127$	−1.05320			−0.0934560			−0.0467280	+	0.998908i	$0.514879\pi$
$128$	−5.37640	+	3.10407i	−0.475211	+	0.274363i
$129$	−8.30583	+	1.20580i	−0.731288	+	0.106165i
$130$		0			0
$131$	−5.22860	−	9.05621i	−0.456825	−	0.791245i	0.541966	−	0.840401i	$-0.317680\pi$
$131$	−5.22860	−	9.05621i	−0.456825	−	0.791245i	−0.998791	+	0.0491560i	$0.984347\pi$
$132$	10.1863	−	8.03317i	0.886603	−	0.699197i
$133$	−7.47194	−	11.8262i	−0.647899	−	1.02546i
$134$		−	2.79562i		−	0.241505i
$135$		0			0
$136$	−9.40343	−	5.42907i	−0.806338	−	0.465539i
$137$	−6.31673	−	3.64697i	−0.539675	−	0.311581i	0.205272	−	0.978705i	$-0.434192\pi$
$137$	−6.31673	−	3.64697i	−0.539675	−	0.311581i	−0.744947	+	0.667124i	$0.767525\pi$
$138$	−3.91969	+	9.82987i	−0.333666	+	0.836774i
$139$			10.8548i			0.920693i	0.887739	+	0.460347i	$0.152275\pi$
$139$			10.8548i			0.920693i	−0.887739	+	0.460347i	$0.847725\pi$
$140$		0			0
$141$	2.08153	+	2.63944i	0.175297	+	0.222281i
$142$	−0.998507	−	1.72946i	−0.0837928	−	0.145133i
$143$	−11.8939	+	20.6008i	−0.994617	+	1.72273i
$144$	0.466740	+	0.442605i	0.0388950	+	0.0368837i
$145$		0			0
$146$	−2.27014			−0.187878
$147$	11.8216	−	2.69247i	0.975031	−	0.222071i
$148$	1.58668			0.130425
$149$	2.54658	−	1.47027i	0.208624	−	0.120449i	−0.392048	−	0.919945i	$-0.628233\pi$
$149$	2.54658	−	1.47027i	0.208624	−	0.120449i	0.600672	+	0.799496i	$0.294900\pi$
$150$		0			0
$151$	−2.49298	+	4.31797i	−0.202876	+	0.351391i	−0.949454	−	0.313907i	$-0.898362\pi$
$151$	−2.49298	+	4.31797i	−0.202876	+	0.351391i	0.746578	+	0.665298i	$0.231695\pi$
$152$	7.59543	+	13.1557i	0.616071	+	1.06707i
$153$	2.64283	−	11.0255i	0.213660	−	0.891356i
$154$	−0.599698	−	15.0276i	−0.0483250	−	1.21096i
$155$		0			0
$156$	7.20676	+	2.87372i	0.577002	+	0.230082i
$157$	−6.14808	−	3.54960i	−0.490671	−	0.283289i	0.234182	−	0.972193i	$-0.424759\pi$
$157$	−6.14808	−	3.54960i	−0.490671	−	0.283289i	−0.724853	+	0.688904i	$0.758092\pi$
$158$	4.77650	+	2.75772i	0.379998	+	0.219392i
$159$	−2.31798	−	0.924303i	−0.183828	−	0.0733020i
$160$		0			0
$161$	−9.57953	−	15.1620i	−0.754973	−	1.19493i
$162$	−3.67762	+	7.23046i	−0.288941	+	0.568079i
$163$	8.84246	+	15.3156i	0.692595	+	1.19961i	0.970985	+	0.239141i	$0.0768659\pi$
$163$	8.84246	+	15.3156i	0.692595	+	1.19961i	−0.278390	+	0.960468i	$0.589801\pi$
$164$	3.88196	−	6.72375i	0.303130	−	0.525036i
$165$		0			0
$166$	−6.66343	+	3.84713i	−0.517182	+	0.298595i
$167$	−10.9235			−0.845287			−0.422643	−	0.906296i	$-0.638898\pi$
$167$	−10.9235			−0.845287			−0.422643	+	0.906296i	$0.638898\pi$
$168$	−12.9438	+	2.40961i	−0.998633	+	0.185905i
$169$	−1.22669			−0.0943611
$170$		0			0
$171$	−10.9145	+	11.5097i	−0.834653	+	0.880168i
$172$	−2.87734	+	4.98370i	−0.219395	+	0.380004i
$173$	−11.5554	−	20.0145i	−0.878539	−	1.52167i	−0.852945	−	0.522001i	$-0.825186\pi$
$173$	−11.5554	−	20.0145i	−0.878539	−	1.52167i	−0.0255936	−	0.999672i	$-0.508148\pi$
$174$	−2.96132	−	3.75504i	−0.224497	−	0.284669i
$175$		0			0
$176$			1.35222i			0.101927i
$177$	2.05578	−	5.15552i	0.154522	−	0.387513i
$178$	0.922304	+	0.532492i	0.0691296	+	0.0399120i
$179$	15.2776	+	8.82051i	1.14190	+	0.659276i	0.946900	−	0.321527i	$-0.104196\pi$
$179$	15.2776	+	8.82051i	1.14190	+	0.659276i	0.194999	+	0.980803i	$0.437530\pi$
$180$		0			0
$181$		−	14.8545i		−	1.10413i	−0.833802	−	0.552064i	$-0.813840\pi$
$181$		−	14.8545i		−	1.10413i	0.833802	−	0.552064i	$-0.186160\pi$
$182$	7.60411	−	4.80438i	0.563654	−	0.356124i
$183$	17.8468	−	14.0744i	1.31927	−	1.04041i
$184$	9.73785	+	16.8665i	0.717884	+	1.24341i
$185$		0			0
$186$	0.624066	−	0.0905986i	0.0457587	−	0.00664301i
$187$	20.6414	−	11.9173i	1.50945	−	0.871481i
$188$	2.30482			0.168097
$189$	−6.25541	−	12.2421i	−0.455014	−	0.890484i
$190$		0			0
$191$	−16.1877	+	9.34599i	−1.17130	+	0.676252i	−0.953987	−	0.299850i	$-0.903064\pi$
$191$	−16.1877	+	9.34599i	−1.17130	+	0.676252i	−0.217316	+	0.976101i	$0.569730\pi$
$192$	9.31407	−	1.35217i	0.672185	−	0.0975843i
$193$	−1.29778	+	2.24781i	−0.0934160	+	0.161801i	−0.908946	−	0.416913i	$-0.863112\pi$
$193$	−1.29778	+	2.24781i	−0.0934160	+	0.161801i	0.815530	+	0.578714i	$0.196445\pi$
$194$	−4.10357	−	7.10759i	−0.294619	−	0.510295i
$195$		0			0
$196$	3.56969	−	7.50776i	0.254978	−	0.536269i
$197$			7.83600i			0.558292i	0.960249	+	0.279146i	$0.0900513\pi$
$197$			7.83600i			0.558292i	−0.960249	+	0.279146i	$0.909949\pi$
$198$	−16.3493	+	4.84921i	−1.16189	+	0.344619i
$199$	3.06915	+	1.77198i	0.217566	+	0.125612i	0.604823	−	0.796360i	$-0.293244\pi$
$199$	3.06915	+	1.77198i	0.217566	+	0.125612i	−0.387256	+	0.921972i	$0.626577\pi$
$200$		0			0
$201$	1.98983	−	4.99012i	0.140351	−	0.351976i
$202$			2.07741i			0.146166i
$203$	8.09819	−	0.323169i	0.568382	−	0.0226820i
$204$	−4.81384	−	6.10410i	−0.337036	−	0.427372i
$205$		0			0
$206$	−3.50920	+	6.07811i	−0.244498	+	0.423482i
$207$	−13.9931	+	14.7562i	−0.972590	+	1.02563i
$208$	−0.700371	+	0.404359i	−0.0485620	+	0.0280373i
$209$	−33.3453			−2.30655
$210$		0			0
$211$	23.9742			1.65045			0.825225	−	0.564804i	$-0.191048\pi$
$211$	23.9742			1.65045			0.825225	+	0.564804i	$0.191048\pi$
$212$	−1.48181	+	0.855523i	−0.101771	+	0.0587576i
$213$	−0.551339	−	3.79776i	−0.0377771	−	0.260218i
$214$	−2.46021	+	4.26121i	−0.168177	+	0.291290i
$215$		0			0
$216$	6.25741	+	13.5543i	0.425763	+	0.922256i
$217$	−0.497028	+	0.946107i	−0.0337404	+	0.0642259i
$218$			5.93674i			0.402087i
$219$	−4.05215	−	1.61581i	−0.273819	−	0.109186i
$220$		0			0
$221$	12.3450	+	7.12736i	0.830412	+	0.479438i
$222$	−1.93742	−	0.772552i	−0.130031	−	0.0518503i
$223$			16.9380i			1.13425i	0.823632	+	0.567125i	$0.191944\pi$
$223$			16.9380i			1.13425i	−0.823632	+	0.567125i	$0.808056\pi$
$224$	−6.83264	+	13.0061i	−0.456525	+	0.869009i
$225$		0			0
$226$	0.0965976	+	0.167312i	0.00642557	+	0.0111294i
$227$	−10.9486	+	18.9635i	−0.726685	+	1.25865i	0.231592	+	0.972813i	$0.425606\pi$
$227$	−10.9486	+	18.9635i	−0.726685	+	1.25865i	−0.958277	+	0.285842i	$0.907727\pi$
$228$	1.56252	+	10.7630i	0.103481	+	0.712800i
$229$	−0.218276	+	0.126022i	−0.0144241	+	0.00832775i	−0.507195	−	0.861831i	$-0.669318\pi$
$229$	−0.218276	+	0.126022i	−0.0144241	+	0.00832775i	0.492771	+	0.870159i	$0.335984\pi$
$230$		0			0
$231$	9.62570	−	27.2508i	0.633325	−	1.79297i
$232$	−8.80103			−0.577816
$233$	12.9405	−	7.47118i	0.847758	−	0.489453i	−0.0121359	−	0.999926i	$-0.503863\pi$
$233$	12.9405	−	7.47118i	0.847758	−	0.489453i	0.859894	+	0.510473i	$0.170530\pi$
$234$	−7.40061	−	7.01791i	−0.483793	−	0.458775i
$235$		0			0
$236$	−1.90281	−	3.29576i	−0.123862	−	0.214535i
$237$	6.56311	+	8.32221i	0.426320	+	0.540586i
$238$	−9.00525	+	0.359366i	−0.583723	+	0.0232943i
$239$			19.5021i			1.26149i	0.775991	+	0.630744i	$0.217250\pi$
$239$			19.5021i			1.26149i	−0.775991	+	0.630744i	$0.782750\pi$
$240$		0			0
$241$	8.54154	+	4.93146i	0.550209	+	0.317663i	0.749206	−	0.662337i	$-0.230435\pi$
$241$	8.54154	+	4.93146i	0.550209	+	0.317663i	−0.198997	+	0.980000i	$0.563768\pi$
$242$	−22.4606	−	12.9676i	−1.44382	−	0.833592i
$243$	−11.7109	+	10.2886i	−0.751253	+	0.660015i
$244$		−	15.5842i		−	0.997678i
$245$		0			0
$246$	−8.01384	+	6.31992i	−0.510944	+	0.402943i
$247$	−9.97138	−	17.2709i	−0.634464	−	1.09892i
$248$	0.580273	−	1.00506i	0.0368474	−	0.0638215i
$249$	−14.6323	+	2.12425i	−0.927286	+	0.134619i
$250$		0			0
$251$	26.5460			1.67557			0.837784	−	0.546002i	$-0.183851\pi$
$251$	26.5460			1.67557			0.837784	+	0.546002i	$0.183851\pi$
$252$	−9.24693	−	1.83000i	−0.582502	−	0.115279i
$253$	−42.7510			−2.68773
$254$	0.822100	−	0.474640i	0.0515832	−	0.0297815i
$255$		0			0
$256$	8.23165	−	14.2576i	0.514478	−	0.891102i
$257$	−7.66481	−	13.2758i	−0.478117	−	0.828124i	0.521568	−	0.853210i	$-0.325347\pi$
$257$	−7.66481	−	13.2758i	−0.478117	−	0.828124i	−0.999685	+	0.0250861i	$0.992014\pi$
$258$	5.93993	−	4.68438i	0.369804	−	0.291637i
$259$	2.98835	−	1.88808i	0.185687	−	0.117319i
$260$		0			0
$261$	−2.61318	−	8.81043i	−0.161752	−	0.545352i
$262$	8.16266	+	4.71271i	0.504291	+	0.291152i
$263$	−19.0437	−	10.9949i	−1.17428	−	0.677972i	−0.219598	−	0.975591i	$-0.570474\pi$
$263$	−19.0437	−	10.9949i	−1.17428	−	0.677972i	−0.954685	+	0.297618i	$0.903808\pi$
$264$	−11.6245	+	29.1520i	−0.715436	+	1.79418i
$265$		0			0
$266$	11.1621	+	5.86389i	0.684391	+	0.359538i
$267$	1.26728	+	1.60695i	0.0775564	+	0.0983438i
$268$	−1.84176	−	3.19002i	−0.112503	−	0.194861i
$269$	14.9395	−	25.8760i	0.910878	−	1.57769i	0.0980517	−	0.995181i	$-0.468739\pi$
$269$	14.9395	−	25.8760i	0.910878	−	1.57769i	0.812826	−	0.582506i	$-0.197928\pi$
$270$		0			0
$271$	−10.7412	+	6.20142i	−0.652480	+	0.376710i	−0.789406	−	0.613872i	$-0.789611\pi$
$271$	−10.7412	+	6.20142i	−0.652480	+	0.376710i	0.136926	+	0.990581i	$0.456278\pi$
$272$	0.810312			0.0491324
$273$	16.9928	−	3.16336i	1.02845	−	0.191456i
$274$	6.57426			0.397166
$275$		0			0
$276$	2.00326	+	13.7989i	0.120582	+	0.830599i
$277$	−4.03409	+	6.98725i	−0.242385	+	0.419823i	−0.961393	−	0.275178i	$-0.911263\pi$
$277$	−4.03409	+	6.98725i	−0.242385	+	0.419823i	0.719008	+	0.695002i	$0.244596\pi$
$278$	−4.89190	−	8.47302i	−0.293397	−	0.508178i
$279$	1.17843	+	0.282472i	0.0705507	+	0.0169112i
$280$		0			0
$281$			17.6732i			1.05430i	0.849773	+	0.527149i	$0.176739\pi$
$281$			17.6732i			1.05430i	−0.849773	+	0.527149i	$0.823261\pi$
$282$	−2.81430	−	1.12221i	−0.167589	−	0.0668268i
$283$	20.5021	+	11.8369i	1.21872	+	0.703629i	0.964644	−	0.263555i	$-0.0848951\pi$
$283$	20.5021	+	11.8369i	1.21872	+	0.703629i	0.254077	+	0.967184i	$0.418228\pi$
$284$	−2.27875	−	1.31564i	−0.135219	−	0.0780686i
$285$		0			0
$286$		−	21.4407i		−	1.26781i
$287$	−0.689694	−	17.2828i	−0.0407113	−	1.02017i
$288$	16.1999	+	3.88315i	0.954586	+	0.228817i
$289$	1.35859	+	2.35315i	0.0799172	+	0.138421i
$290$		0			0
$291$	−2.26584	−	15.6077i	−0.132826	−	0.914938i
$292$	−2.59041	+	1.49557i	−0.151592	+	0.0875217i
$293$	−2.70804			−0.158205			−0.0791026	−	0.996866i	$-0.525205\pi$
$293$	−2.70804			−0.158205			−0.0791026	+	0.996866i	$0.525205\pi$
$294$	−8.01428	+	7.42928i	−0.467402	+	0.433285i
$295$		0			0
$296$	−3.32430	+	1.91928i	−0.193221	+	0.111556i
$297$	−32.6347	−	2.98114i	−1.89365	−	0.172983i
$298$	−1.32520	+	2.29532i	−0.0767670	+	0.132964i
$299$	−12.7840	−	22.1425i	−0.739317	−	1.28053i
$300$		0			0
$301$	0.511207	+	12.8102i	0.0294655	+	0.738366i
$302$		−	4.49401i		−	0.258601i
$303$	−1.47863	+	3.70814i	−0.0849452	+	0.213027i
$304$	−0.981769	−	0.566825i	−0.0563083	−	0.0325096i
$305$		0			0
$306$	2.90587	+	9.79726i	0.166118	+	0.560072i
$307$		−	5.49592i		−	0.313669i	−0.987625	−	0.156834i	$-0.949871\pi$
$307$		−	5.49592i		−	0.313669i	0.987625	−	0.156834i	$-0.0501289\pi$
$308$	−10.5845	−	16.7526i	−0.603109	−	0.954569i
$309$	−10.5900	+	8.35157i	−0.602446	+	0.475104i
$310$		0			0
$311$	10.9235	−	18.9201i	0.619416	−	1.07286i	−0.370177	−	0.928961i	$-0.620703\pi$
$311$	10.9235	−	18.9201i	0.619416	−	1.07286i	0.989593	−	0.143898i	$-0.0459637\pi$
$312$	−18.5752	+	2.69664i	−1.05161	+	0.152667i
$313$	−21.2964	+	12.2955i	−1.20375	+	0.694983i	−0.961386	−	0.275203i	$-0.911255\pi$
$313$	−21.2964	+	12.2955i	−1.20375	+	0.694983i	−0.242360	+	0.970186i	$0.577921\pi$
$314$	6.39874			0.361102
$315$		0			0
$316$	7.26715			0.408809
$317$	20.7457	−	11.9775i	1.16520	−	0.672726i	0.212652	−	0.977128i	$-0.431790\pi$
$317$	20.7457	−	11.9775i	1.16520	−	0.672726i	0.952544	+	0.304402i	$0.0984565\pi$
$318$	2.22592	−	0.323147i	0.124823	−	0.0181212i
$319$	9.65954	−	16.7308i	0.540830	−	0.936746i
$320$		0			0
$321$	−7.42441	+	5.85507i	−0.414390	+	0.326798i
$322$	14.3105	+	7.51791i	0.797496	+	0.418956i
$323$			19.9821i			1.11183i
$324$	0.566985	+	10.6733i	0.0314992	+	0.592963i
$325$		0			0
$326$	−13.8044	−	7.97000i	−0.764557	−	0.441417i
$327$	−4.22557	+	10.5969i	−0.233674	+	0.586013i
$328$			18.7828i			1.03711i
$329$	4.34089	−	2.74263i	0.239321	−	0.151206i
$330$		0			0
$331$	−13.5511	−	23.4712i	−0.744837	−	1.29009i	−0.950271	−	0.311424i	$-0.899194\pi$
$331$	−13.5511	−	23.4712i	−0.744837	−	1.29009i	0.205434	−	0.978671i	$-0.434139\pi$
$332$	−5.06899	+	8.77975i	−0.278197	+	0.481852i
$333$	−2.90837	−	2.75798i	−0.159378	−	0.151136i
$334$	8.52664	−	4.92286i	0.466557	−	0.269367i
$335$		0			0
$336$	0.746631	−	0.638708i	0.0407321	−	0.0348444i
$337$	3.19846			0.174231			0.0871155	−	0.996198i	$-0.472235\pi$
$337$	3.19846			0.174231			0.0871155	+	0.996198i	$0.472235\pi$
$338$	0.957529	−	0.552830i	0.0520827	−	0.0300700i
$339$	0.0533377	+	0.367403i	0.00289690	+	0.0199546i
$340$		0			0
$341$	1.27375	+	2.20620i	0.0689776	+	0.119473i
$342$	3.33258	−	13.9030i	0.180205	−	0.751788i
$343$	−2.21077	−	18.3878i	−0.119370	−	0.992850i
$344$		−	13.9220i		−	0.750622i
$345$		0			0
$346$	18.0397	+	10.4152i	0.969821	+	0.559926i
$347$	28.2567	+	16.3140i	1.51690	+	0.875783i	0.999803	+	0.0198563i	$0.00632087\pi$
$347$	28.2567	+	16.3140i	1.51690	+	0.875783i	0.517097	+	0.855927i	$0.327012\pi$
$348$	−5.85292	−	2.33387i	−0.313750	−	0.125109i
$349$			32.4849i			1.73888i	0.494041	+	0.869439i	$0.335519\pi$
$349$			32.4849i			1.73888i	−0.494041	+	0.869439i	$0.664481\pi$
$350$		0			0
$351$	−8.21481	−	17.7943i	−0.438474	−	0.949790i
$352$	17.5103	+	30.3287i	0.933301	+	1.61653i
$353$	3.33584	−	5.77784i	0.177549	−	0.307523i	−0.763492	−	0.645818i	$-0.776517\pi$
$353$	3.33584	−	5.77784i	0.177549	−	0.307523i	0.941040	+	0.338294i	$0.109850\pi$
$354$	0.718725	+	4.95075i	0.0381998	+	0.263130i
$355$		0			0
$356$	1.40323			0.0743709
$357$	−16.3300	−	5.76817i	−0.864273	−	0.305284i
$358$	−15.9004			−0.840364
$359$	−14.0322	+	8.10148i	−0.740590	+	0.427580i	−0.822284	−	0.569078i	$-0.807300\pi$
$359$	−14.0322	+	8.10148i	−0.740590	+	0.427580i	0.0816940	+	0.996657i	$0.473967\pi$
$360$		0			0
$361$	4.47774	−	7.75567i	0.235671	−	0.408193i
$362$	6.69443	+	11.5951i	0.351852	+	0.609425i
$363$	−30.8618	−	39.1337i	−1.61982	−	2.05398i
$364$	5.51175	−	10.4918i	0.288894	−	0.549918i
$365$		0			0
$366$	−7.58793	+	19.0291i	−0.396627	+	0.994669i
$367$	14.9080	+	8.60716i	0.778193	+	0.449290i	0.835789	−	0.549050i	$-0.185010\pi$
$367$	14.9080	+	8.60716i	0.778193	+	0.449290i	−0.0575965	+	0.998340i	$0.518344\pi$
$368$	−1.25869	−	0.726708i	−0.0656140	−	0.0378823i
$369$	−18.8028	+	5.57693i	−0.978836	+	0.290324i
$370$		0			0
$371$	−1.77280	+	3.37457i	−0.0920391	+	0.175199i
$372$	0.652421	−	0.514515i	0.0338264	−	0.0266764i
$373$	6.16568	+	10.6793i	0.319247	+	0.552952i	0.980331	−	0.197360i	$-0.0632368\pi$
$373$	6.16568	+	10.6793i	0.319247	+	0.552952i	−0.661084	+	0.750312i	$0.729903\pi$
$374$	−10.7415	+	18.6048i	−0.555428	+	0.962030i
$375$		0			0
$376$	−4.82889	+	2.78796i	−0.249031	+	0.143778i
$377$	11.5541			0.595067
$378$	10.3999	+	6.73683i	0.534916	+	0.346505i
$379$	−3.57576			−0.183675			−0.0918373	−	0.995774i	$-0.529274\pi$
$379$	−3.57576			−0.183675			−0.0918373	+	0.995774i	$0.529274\pi$
$380$		0			0
$381$	1.80526	−	0.262079i	0.0924864	−	0.0134267i
$382$	8.42384	−	14.5905i	0.431001	−	0.746516i
$383$	11.5654	+	20.0319i	0.590965	+	1.02358i	0.994103	+	0.108442i	$0.0345861\pi$
$383$	11.5654	+	20.0319i	0.590965	+	1.02358i	−0.403138	+	0.915139i	$0.632081\pi$
$384$	8.44317	−	6.65850i	0.430864	−	0.339790i
$385$		0			0
$386$		−	2.33946i		−	0.119075i
$387$	13.9368	−	4.13367i	0.708449	−	0.210126i
$388$	−9.36499	−	5.40688i	−0.475435	−	0.274493i
$389$	14.7169	+	8.49679i	0.746175	+	0.430804i	0.824310	−	0.566138i	$-0.191563\pi$
$389$	14.7169	+	8.49679i	0.746175	+	0.430804i	−0.0781352	+	0.996943i	$0.524897\pi$
$390$		0			0
$391$			25.6184i			1.29558i
$392$	1.60261	+	20.0477i	0.0809440	+	1.01256i
$393$	11.2158	+	14.2220i	0.565763	+	0.717405i
$394$	−3.53142	−	6.11660i	−0.177910	−	0.308150i
$395$		0			0
$396$	−15.4612	+	16.3043i	−0.776952	+	0.819321i
$397$	18.7837	−	10.8448i	0.942726	−	0.544283i	0.0519125	−	0.998652i	$-0.483468\pi$
$397$	18.7837	−	10.8448i	0.942726	−	0.544283i	0.890814	+	0.454368i	$0.150135\pi$
$398$	−3.19428			−0.160115
$399$	15.7504	+	18.4117i	0.788504	+	0.921739i
$400$		0			0
$401$	−0.425230	+	0.245507i	−0.0212350	+	0.0122600i	−0.510580	−	0.859830i	$-0.670569\pi$
$401$	−0.425230	+	0.245507i	−0.0212350	+	0.0122600i	0.489345	+	0.872090i	$0.337236\pi$
$402$	0.695666	+	4.79192i	0.0346967	+	0.238999i
$403$	−0.761790	+	1.31946i	−0.0379475	+	0.0657270i
$404$	1.36860	+	2.37049i	0.0680906	+	0.117936i
$405$		0			0
$406$	−6.17562	+	3.90184i	−0.306491	+	0.193645i
$407$		−	8.42601i		−	0.417662i
$408$	17.4692	+	6.96592i	0.864856	+	0.344864i
$409$	24.2867	+	14.0219i	1.20090	+	0.693339i	0.960755	−	0.277399i	$-0.0894723\pi$
$409$	24.2867	+	14.0219i	1.20090	+	0.693339i	0.240143	+	0.970738i	$0.422806\pi$
$410$		0			0
$411$	11.7349	+	4.67933i	0.578840	+	0.230815i
$412$			9.24747i			0.455590i
$413$	−7.50553	−	3.94295i	−0.369323	−	0.194020i
$414$	4.27260	−	17.8246i	0.209987	−	0.876031i
$415$		0			0
$416$	−10.4723	+	18.1386i	−0.513448	+	0.889319i
$417$	−2.70113	−	18.6060i	−0.132275	−	0.911142i
$418$	26.0286	−	15.0276i	1.27310	−	0.735025i
$419$	−3.44153			−0.168130			−0.0840649	−	0.996460i	$-0.526790\pi$
$419$	−3.44153			−0.168130			−0.0840649	+	0.996460i	$0.526790\pi$
$420$		0			0
$421$	18.7964			0.916078			0.458039	−	0.888932i	$-0.348552\pi$
$421$	18.7964			0.916078			0.458039	+	0.888932i	$0.348552\pi$
$422$	−18.7137	+	10.8044i	−0.910968	+	0.525948i
$423$	−4.22472	−	4.00625i	−0.205413	−	0.194791i
$424$	2.06972	−	3.58485i	0.100514	−	0.174096i
$425$		0			0
$426$	2.14188	+	2.71597i	0.103775	+	0.131589i
$427$	−18.5445	−	29.3512i	−0.897432	−	1.42041i
$428$			6.48316i			0.313375i
$429$	15.2608	−	38.2712i	0.736796	−	1.84775i
$430$		0			0
$431$	−5.95390	−	3.43749i	−0.286789	−	0.165578i	0.349704	−	0.936860i	$-0.386282\pi$
$431$	−5.95390	−	3.43749i	−0.286789	−	0.165578i	−0.636493	+	0.771282i	$0.719616\pi$
$432$	−0.910170	−	0.642516i	−0.0437906	−	0.0309131i
$433$		−	15.2776i		−	0.734193i	−0.930183	−	0.367096i	$-0.880352\pi$
$433$		−	15.2776i		−	0.734193i	0.930183	−	0.367096i	$-0.119648\pi$
$434$	−0.0384100	−	0.962503i	−0.00184374	−	0.0462016i
$435$		0			0
$436$	3.91113	+	6.77428i	0.187309	+	0.324429i
$437$	17.9204	−	31.0391i	0.857249	−	1.48480i
$438$	3.89121	−	0.564905i	0.185929	−	0.0269922i
$439$	33.3367	−	19.2469i	1.59107	−	0.918606i	0.597948	−	0.801535i	$-0.295983\pi$
$439$	33.3367	−	19.2469i	1.59107	−	0.918606i	0.993124	−	0.117071i	$-0.0373505\pi$
$440$		0			0
$441$	−19.5932	+	7.55682i	−0.933011	+	0.359849i
$442$	−12.8483			−0.611129
$443$	3.33990	−	1.92829i	0.158683	−	0.0916158i	−0.418556	−	0.908191i	$-0.637464\pi$
$443$	3.33990	−	1.92829i	0.158683	−	0.0916158i	0.577239	+	0.816575i	$0.304130\pi$
$444$	−2.71970	+	0.394833i	−0.129071	+	0.0187379i
$445$		0			0
$446$	−7.63337	−	13.2214i	−0.361450	−	0.626050i
$447$	−3.99919	+	3.15386i	−0.189155	+	0.149172i
$448$	−0.573262	−	14.3652i	−0.0270841	−	0.678691i
$449$			2.52159i			0.119001i	0.998228	+	0.0595005i	$0.0189508\pi$
$449$			2.52159i			0.119001i	−0.998228	+	0.0595005i	$0.981049\pi$
$450$		0			0
$451$	−35.7062	−	20.6150i	−1.68134	−	0.970721i
$452$	0.220451	+	0.127277i	0.0103691	+	0.00598662i
$453$	3.19868	−	8.02171i	0.150287	−	0.376893i
$454$		−	19.7367i		−	0.926288i
$455$		0			0
$456$	−16.2929	−	20.6598i	−0.762984	−	0.967486i
$457$	−4.65226	−	8.05795i	−0.217623	−	0.376935i	0.736457	−	0.676484i	$-0.236497\pi$
$457$	−4.65226	−	8.05795i	−0.217623	−	0.376935i	−0.954081	+	0.299549i	$0.903164\pi$
$458$	0.113588	−	0.196739i	0.00530760	−	0.00919303i
$459$	−1.78643	+	19.5562i	−0.0833836	+	0.912805i
$460$		0			0
$461$	11.3898			0.530477			0.265238	−	0.964183i	$-0.414549\pi$
$461$	11.3898			0.530477			0.265238	+	0.964183i	$0.414549\pi$
$462$	4.76743	+	25.6094i	0.221801	+	1.19146i
$463$	0.322319			0.0149795			0.00748973	−	0.999972i	$-0.497616\pi$
$463$	0.322319			0.0149795			0.00748973	+	0.999972i	$0.497616\pi$
$464$	0.568801	−	0.328398i	0.0264059	−	0.0152455i
$465$		0			0
$466$	−6.73402	+	11.6637i	−0.311947	+	0.540309i
$467$	11.6576	+	20.1915i	0.539449	+	0.934353i	0.998934	+	0.0461675i	$0.0147008\pi$
$467$	11.6576	+	20.1915i	0.539449	+	0.934353i	−0.459485	+	0.888186i	$0.651966\pi$
$468$	−13.0681	−	3.13245i	−0.604072	−	0.144798i
$469$	−7.26473	−	3.81645i	−0.335454	−	0.176227i
$470$		0			0
$471$	11.4216	+	4.55440i	0.526280	+	0.209856i
$472$	7.97323	+	4.60334i	0.366997	+	0.211886i
$473$	26.4657	+	15.2800i	1.21690	+	0.702575i
$474$	−8.87355	−	3.53836i	−0.407576	−	0.162522i
$475$		0			0
$476$	−10.0389	+	6.34274i	−0.460134	+	0.290719i
$477$	4.20322	+	1.00752i	0.192452	+	0.0461312i
$478$	−8.78895	−	15.2229i	−0.401997	−	0.696280i
$479$	0.316556	−	0.548292i	0.0144638	−	0.0250521i	−0.858703	−	0.512474i	$-0.828729\pi$
$479$	0.316556	−	0.548292i	0.0144638	−	0.0250521i	0.873167	+	0.487422i	$0.162063\pi$
$480$		0			0
$481$	4.36418	−	2.51966i	0.198990	−	0.114887i
$482$	−8.88978			−0.404918
$483$	20.1930	+	23.6051i	0.918815	+	1.07407i
$484$	−34.1724			−1.55329
$485$		0			0
$486$	4.50451	−	13.3087i	0.204329	−	0.603697i
$487$	10.8253	−	18.7500i	0.490541	−	0.849642i	−0.509400	−	0.860530i	$-0.670132\pi$
$487$	10.8253	−	18.7500i	0.490541	−	0.849642i	0.999941	+	0.0108880i	$0.00346582\pi$
$488$	18.8510	+	32.6509i	0.853345	+	1.47804i
$489$	−18.9679	−	24.0518i	−0.857756	−	1.08766i
$490$		0			0
$491$		−	36.1608i		−	1.63191i	−0.578112	−	0.815957i	$-0.696211\pi$
$491$		−	36.1608i		−	1.63191i	0.578112	−	0.815957i	$-0.303789\pi$
$492$	−4.98085	+	12.4910i	−0.224554	+	0.563140i
$493$	−10.0259	−	5.78844i	−0.451543	−	0.260698i
$494$	15.5669	+	8.98754i	0.700387	+	0.404368i
$495$		0			0
$496$			0.0866082i			0.00388882i
$497$	−5.85732	+	0.233744i	−0.262737	+	0.0104849i
$498$	10.4643	−	8.25244i	0.468918	−	0.369801i
$499$	4.50676	+	7.80593i	0.201750	+	0.349442i	0.949092	−	0.314998i	$-0.102004\pi$
$499$	4.50676	+	7.80593i	0.201750	+	0.349442i	−0.747342	+	0.664439i	$0.768670\pi$
$500$		0			0
$501$	18.7238	−	2.71822i	0.836518	−	0.121441i
$502$	−20.7212	+	11.9634i	−0.924832	+	0.533952i
$503$	18.9044			0.842907			0.421453	−	0.906850i	$-0.361520\pi$
$503$	18.9044			0.842907			0.421453	+	0.906850i	$0.361520\pi$
$504$	21.5871	−	7.35121i	0.961565	−	0.327449i
$505$		0			0
$506$	33.3704	−	19.2664i	1.48350	−	0.856497i
$507$	2.10265	−	0.305252i	0.0933822	−	0.0135567i
$508$	0.625387	−	1.08320i	0.0277471	−	0.0480593i
$509$	19.6636	+	34.0584i	0.871574	+	1.50961i	0.860368	+	0.509673i	$0.170234\pi$
$509$	19.6636	+	34.0584i	0.871574	+	1.50961i	0.0112055	+	0.999937i	$0.496433\pi$
$510$		0			0
$511$	−3.09909	+	5.89921i	−0.137096	+	0.260966i
$512$			2.42264i			0.107067i
$513$	15.8443	−	22.4445i	0.699542	−	0.990950i
$514$	11.9659	+	6.90854i	0.527795	+	0.304723i
$515$		0			0
$516$	3.69185	−	9.25848i	0.162525	−	0.407582i
$517$		−	12.2397i		−	0.538300i
$518$	−1.48174	+	2.82054i	−0.0651040	+	0.123927i
$519$	24.7873	+	31.4310i	1.08804	+	1.37967i
$520$		0			0
$521$	−8.61869	+	14.9280i	−0.377592	+	0.654008i	−0.990711	−	0.135982i	$-0.956581\pi$
$521$	−8.61869	+	14.9280i	−0.377592	+	0.654008i	0.613120	+	0.789990i	$0.289914\pi$
$522$	6.01035	+	5.69955i	0.263066	+	0.249462i
$523$	32.7149	−	18.8880i	1.43052	−	0.825914i	0.433364	−	0.901219i	$-0.357326\pi$
$523$	32.7149	−	18.8880i	1.43052	−	0.825914i	0.997161	+	0.0753051i	$0.0239931\pi$
$524$	12.4190			0.542525
$525$		0			0
$526$	19.8201			0.864196
$527$	1.32206	−	0.763291i	0.0575898	−	0.0332495i
$528$	−0.336488	−	2.31781i	−0.0146438	−	0.100870i
$529$	11.4752	−	19.8756i	0.498920	−	0.864156i
$530$		0			0
$531$	−2.24087	+	9.34855i	−0.0972455	+	0.405693i
$532$	16.6000	−	0.662443i	0.719699	−	0.0287206i
$533$		−	24.6583i		−	1.06807i
$534$	−1.71341	−	0.683228i	−0.0741465	−	0.0295662i
$535$		0			0
$536$	7.71742	+	4.45565i	0.333342	+	0.192455i
$537$	−28.3819	−	11.3174i	−1.22477	−	0.488381i
$538$			26.9309i			1.16108i
$539$	−39.8697	−	18.9567i	−1.71731	−	0.816521i
$540$		0			0
$541$	−9.89533	−	17.1392i	−0.425433	−	0.736872i	0.571027	−	0.820931i	$-0.306545\pi$
$541$	−9.89533	−	17.1392i	−0.425433	−	0.736872i	−0.996461	+	0.0840587i	$0.973212\pi$
$542$	5.58955	−	9.68138i	0.240092	−	0.415851i
$543$	3.69642	+	25.4619i	0.158629	+	1.09267i
$544$	18.1744	−	10.4930i	0.779219	−	0.449882i
$545$		0			0
$546$	−11.8385	+	10.1273i	−0.506642	+	0.433409i
$547$	8.91454			0.381158			0.190579	−	0.981672i	$-0.438963\pi$
$547$	8.91454			0.381158			0.190579	+	0.981672i	$0.438963\pi$
$548$	7.50174	−	4.33113i	0.320459	−	0.185017i
$549$	−27.0886	+	28.5658i	−1.15611	+	1.21916i
$550$		0			0
$551$	8.09819	+	14.0265i	0.344995	+	0.597548i
$552$	−20.8886	−	26.4873i	−0.889076	−	1.12737i
$553$	13.6869	−	8.64757i	0.582026	−	0.367732i
$554$		−	7.27212i		−	0.308963i
$555$		0			0
$556$	−11.1641	−	6.44558i	−0.473462	−	0.273354i
$557$	18.1599	+	10.4847i	0.769462	+	0.444249i	0.832683	−	0.553751i	$-0.186804\pi$
$557$	18.1599	+	10.4847i	0.769462	+	0.444249i	−0.0632208	+	0.998000i	$0.520137\pi$
$558$	−1.04716	+	0.310587i	−0.0443296	+	0.0131482i
$559$			18.2769i			0.773032i
$560$		0			0
$561$	−32.4155	+	25.5637i	−1.36859	+	1.07930i
$562$	−7.96474	−	13.7953i	−0.335972	−	0.581921i
$563$	9.04347	−	15.6638i	0.381137	−	0.660148i	−0.610088	−	0.792333i	$-0.708866\pi$
$563$	9.04347	−	15.6638i	0.381137	−	0.660148i	0.991225	+	0.132185i	$0.0421993\pi$
$564$	−3.95066	+	0.573536i	−0.166353	+	0.0241502i
$565$		0			0
$566$	−21.3379			−0.896900
$567$	13.7686	+	19.4274i	0.578228	+	0.815875i
$568$	6.36568			0.267098
$569$	22.0888	−	12.7530i	0.926010	−	0.534632i	0.0404626	−	0.999181i	$-0.487117\pi$
$569$	22.0888	−	12.7530i	0.926010	−	0.534632i	0.885547	+	0.464549i	$0.153784\pi$
$570$		0			0
$571$	−19.8853	+	34.4424i	−0.832175	+	1.44137i	0.0641352	+	0.997941i	$0.479571\pi$
$571$	−19.8853	+	34.4424i	−0.832175	+	1.44137i	−0.896310	+	0.443428i	$0.853762\pi$
$572$	−14.1252	−	24.4655i	−0.590603	−	1.02295i
$573$	25.4214	−	20.0480i	1.06199	−	0.837516i
$574$	8.32714	+	13.1797i	0.347568	+	0.550112i
$575$		0			0
$576$	−15.6286	+	4.63545i	−0.651192	+	0.193144i
$577$	1.72826	+	0.997811i	0.0719484	+	0.0415394i	0.535543	−	0.844508i	$-0.320107\pi$
$577$	1.72826	+	0.997811i	0.0719484	+	0.0415394i	−0.463594	+	0.886048i	$0.653440\pi$
$578$	−2.12097	−	1.22454i	−0.0882208	−	0.0509343i
$579$	1.66515	−	4.17588i	0.0692011	−	0.173544i
$580$		0			0
$581$	0.900590	+	22.5676i	0.0373628	+	0.936262i
$582$	8.80252	+	11.1619i	0.364876	+	0.462674i
$583$	4.54322	+	7.86909i	0.188161	+	0.325904i
$584$	3.61815	−	6.26682i	0.149720	−	0.259323i
$585$		0			0
$586$	2.11383	−	1.22042i	0.0873216	−	0.0504152i
$587$	−27.4257			−1.13198			−0.565989	−	0.824413i	$-0.691506\pi$
$587$	−27.4257			−1.13198			−0.565989	+	0.824413i	$0.691506\pi$
$588$	−4.25049	+	13.7572i	−0.175287	+	0.567338i
$589$	−2.13573			−0.0880013
$590$		0			0
$591$	−1.94992	−	13.4315i	−0.0802090	−	0.552500i
$592$	0.143231	−	0.248083i	0.00588674	−	0.0101961i
$593$	0.606763	+	1.05094i	0.0249168	+	0.0431571i	0.878215	−	0.478266i	$-0.158735\pi$
$593$	0.606763	+	1.05094i	0.0249168	+	0.0431571i	−0.853298	+	0.521423i	$0.825401\pi$
$594$	26.8174	−	12.3803i	1.10033	−	0.507971i
$595$		0			0
$596$			3.49218i			0.143045i
$597$	−5.70172	−	2.27358i	−0.233356	−	0.0930514i
$598$	19.9578	+	11.5226i	0.816134	+	0.471195i
$599$	−32.9617	−	19.0304i	−1.34678	−	0.777563i	−0.358986	−	0.933343i	$-0.616878\pi$
$599$	−32.9617	−	19.0304i	−1.34678	−	0.777563i	−0.987792	+	0.155780i	$0.950211\pi$
$600$		0			0
$601$		−	8.32414i		−	0.339549i	−0.985483	−	0.169774i	$-0.945696\pi$
$601$		−	8.32414i		−	0.339549i	0.985483	−	0.169774i	$-0.0543039\pi$
$602$	−6.17215	−	9.76894i	−0.251558	−	0.398152i
$603$	−2.16898	+	9.04862i	−0.0883275	+	0.368488i
$604$	−2.96066	−	5.12802i	−0.120468	−	0.208656i
$605$		0			0
$606$	−0.516947	−	3.56086i	−0.0209995	−	0.144650i
$607$	−26.1996	+	15.1263i	−1.06341	+	0.613959i	−0.926373	−	0.376607i	$-0.877091\pi$
$607$	−26.1996	+	15.1263i	−1.06341	+	0.613959i	−0.137036	+	0.990566i	$0.543758\pi$
$608$	−29.3599			−1.19070
$609$	−13.8006	+	2.56911i	−0.559227	+	0.104105i
$610$		0			0
$611$	6.33943	−	3.66007i	0.256466	−	0.148071i
$612$	9.77028	+	9.26504i	0.394940	+	0.374517i
$613$	−1.41851	+	2.45694i	−0.0572933	+	0.0992349i	−0.893249	−	0.449561i	$-0.851580\pi$
$613$	−1.41851	+	2.45694i	−0.0572933	+	0.0992349i	0.835956	+	0.548796i	$0.184914\pi$
$614$	2.47683	+	4.28999i	0.0999566	+	0.173130i
$615$		0			0
$616$	42.4402	+	22.2955i	1.70996	+	0.898313i
$617$			23.3983i			0.941979i	0.882139	+	0.470990i	$0.156103\pi$
$617$			23.3983i			0.941979i	−0.882139	+	0.470990i	$0.843897\pi$
$618$	4.50257	−	11.2916i	0.181120	−	0.454216i
$619$	−34.7980	−	20.0907i	−1.39865	−	0.807511i	−0.404400	−	0.914582i	$-0.632519\pi$
$619$	−34.7980	−	20.0907i	−1.39865	−	0.807511i	−0.994251	+	0.107071i	$0.965853\pi$
$620$		0			0
$621$	20.3134	−	28.7754i	0.815150	−	1.15472i
$622$			19.6914i			0.789555i
$623$	2.64283	−	1.66978i	0.105883	−	0.0668981i
$624$	1.09987	−	0.867386i	0.0440301	−	0.0347232i
$625$		0			0
$626$	11.0823	−	19.1952i	0.442939	−	0.767194i
$627$	57.1567	−	8.29771i	2.28262	−	0.331378i
$628$	7.30146	−	4.21550i	0.291360	−	0.168217i
$629$	−5.04925			−0.201327
$630$		0			0
$631$	−22.9329			−0.912945			−0.456473	−	0.889737i	$-0.650887\pi$
$631$	−22.9329			−0.912945			−0.456473	+	0.889737i	$0.650887\pi$
$632$	−15.2256	+	8.79049i	−0.605641	+	0.349667i
$633$	−41.0937	+	5.96577i	−1.63333	+	0.237118i
$634$	−10.7958	+	18.6988i	−0.428754	+	0.742624i
$635$		0			0
$636$	2.32705	−	1.83517i	0.0922737	−	0.0727694i
$637$	−2.10393	−	26.3188i	−0.0833607	−	1.04279i
$638$			17.4129i			0.689384i
$639$	1.89008	+	6.37248i	0.0747704	+	0.252091i
$640$		0			0
$641$	−1.70493	−	0.984339i	−0.0673405	−	0.0388791i	0.465952	−	0.884810i	$-0.345712\pi$
$641$	−1.70493	−	0.984339i	−0.0673405	−	0.0388791i	−0.533292	+	0.845931i	$0.679045\pi$
$642$	3.15664	−	7.91627i	0.124583	−	0.312430i
$643$			18.9036i			0.745483i	0.927935	+	0.372742i	$0.121582\pi$
$643$			18.9036i			0.745483i	−0.927935	+	0.372742i	$0.878418\pi$
$644$	21.2823	−	0.849297i	0.838638	−	0.0334670i
$645$		0			0
$646$	−9.00525	−	15.5975i	−0.354307	−	0.613677i
$647$	−3.33350	+	5.77380i	−0.131054	+	0.226991i	−0.924083	−	0.382192i	$-0.875169\pi$
$647$	−3.33350	+	5.77380i	−0.131054	+	0.226991i	0.793029	+	0.609183i	$0.208503\pi$
$648$	−14.0986	−	21.6761i	−0.553845	−	0.851519i
$649$	−17.5020	+	10.1048i	−0.687012	+	0.396647i
$650$		0			0
$651$	0.616516	−	1.74539i	0.0241632	−	0.0684071i
$652$	−21.0026			−0.822525
$653$	−29.3074	+	16.9206i	−1.14689	+	0.662156i	−0.948127	−	0.317892i	$-0.897025\pi$
$653$	−29.3074	+	16.9206i	−1.14689	+	0.662156i	−0.198761	+	0.980048i	$0.563692\pi$
$654$	−1.47731	−	10.1761i	−0.0577673	−	0.397915i
$655$		0			0
$656$	−0.700852	−	1.21391i	−0.0273637	−	0.0473953i
$657$	7.34780	+	1.76129i	0.286665	+	0.0687143i
$658$	−2.15239	+	4.09713i	−0.0839088	+	0.159723i
$659$			22.0797i			0.860101i	0.902805	+	0.430051i	$0.141504\pi$
$659$			22.0797i			0.860101i	−0.902805	+	0.430051i	$0.858496\pi$
$660$		0			0
$661$	27.1770	+	15.6907i	1.05706	+	0.610296i	0.924619	−	0.380894i	$-0.124384\pi$
$661$	27.1770	+	15.6907i	1.05706	+	0.610296i	0.132445	+	0.991190i	$0.457717\pi$
$662$	21.1554	+	12.2141i	0.822227	+	0.474713i
$663$	−22.9339	−	9.14495i	−0.890677	−	0.355160i
$664$		−	24.5262i		−	0.951802i
$665$		0			0
$666$	3.51314	+	0.842108i	0.136131	+	0.0326310i
$667$	10.3824	+	17.9829i	0.402009	+	0.696301i
$668$	6.48638	−	11.2347i	0.250965	−	0.434685i
$669$	−4.21487	−	29.0330i	−0.162956	−	1.12248i
$670$		0			0
$671$	−82.7594			−3.19489
$672$	8.47525	−	23.9938i	0.326940	−	0.925582i
$673$	−40.5686			−1.56380			−0.781902	−	0.623401i	$-0.785751\pi$
$673$	−40.5686			−1.56380			−0.781902	+	0.623401i	$0.785751\pi$
$674$	−2.49664	+	1.44144i	−0.0961671	+	0.0555221i
$675$		0			0
$676$	0.728410	−	1.26164i	0.0280158	−	0.0485248i
$677$	−19.9031	−	34.4733i	−0.764940	−	1.32491i	−0.940278	−	0.340407i	$-0.889435\pi$
$677$	−19.9031	−	34.4733i	−0.764940	−	1.32491i	0.175338	−	0.984508i	$-0.443898\pi$
$678$	−0.207210	−	0.262749i	−0.00795786	−	0.0100908i
$679$	−24.0719	+	0.960621i	−0.923794	+	0.0368653i
$680$		0			0
$681$	14.0479	−	35.2295i	0.538317	−	1.35000i
$682$	−1.98852	−	1.14808i	−0.0761445	−	0.0439621i
$683$	−19.9121	−	11.4962i	−0.761915	−	0.439892i	0.0680680	−	0.997681i	$-0.478317\pi$
$683$	−19.9121	−	11.4962i	−0.761915	−	0.439892i	−0.829983	+	0.557789i	$0.811650\pi$
$684$	−5.35658	−	18.0599i	−0.204814	−	0.690538i
$685$		0			0
$686$	10.0125	+	13.3568i	0.382277	+	0.509965i
$687$	0.342784	−	0.270328i	0.0130780	−	0.0103137i
$688$	0.519478	+	0.899762i	0.0198049	+	0.0343031i
$689$	−2.71715	+	4.70625i	−0.103515	+	0.179294i
$690$		0			0
$691$	20.7325	−	11.9699i	0.788702	−	0.455358i	−0.0508031	−	0.998709i	$-0.516178\pi$
$691$	20.7325	−	11.9699i	0.788702	−	0.455358i	0.839506	+	0.543351i	$0.182845\pi$
$692$	27.4463			1.04335
$693$	−9.71811	+	49.1054i	−0.369161	+	1.86536i
$694$	−29.4087			−1.11634
$695$		0			0
$696$	15.0857	−	2.19006i	0.571822	−	0.0830141i
$697$	−12.3534	+	21.3968i	−0.467920	+	0.810461i
$698$	−14.6399	−	25.3570i	−0.554127	−	0.959776i
$699$	−20.3219	+	16.0263i	−0.768644	+	0.606172i
$700$		0			0
$701$		−	7.70996i		−	0.291201i	−0.989343	−	0.145601i	$-0.953489\pi$
$701$		−	7.70996i		−	0.291201i	0.989343	−	0.145601i	$-0.0465115\pi$
$702$	14.4316	+	10.1877i	0.544685	+	0.384510i
$703$	6.11765	+	3.53202i	0.230731	+	0.133213i
$704$	−29.6784	−	17.1348i	−1.11855	−	0.645793i
$705$		0			0
$706$			6.01340i			0.226317i
$707$	5.39839	+	2.83599i	0.203027	+	0.106658i
$708$	4.08169	+	5.17570i	0.153399	+	0.194515i
$709$	1.62353	+	2.81203i	0.0609729	+	0.105608i	0.894901	−	0.446266i	$-0.147246\pi$
$709$	1.62353	+	2.81203i	0.0609729	+	0.105608i	−0.833928	+	0.551874i	$0.813913\pi$
$710$		0			0
$711$	−13.3206	−	12.6318i	−0.499562	−	0.473729i
$712$	−2.93993	+	1.69737i	−0.110179	+	0.0636117i
$713$	−2.73815			−0.102545
$714$	15.3463	−	2.85686i	0.574321	−	0.106915i
$715$		0			0
$716$	−18.1436	+	10.4752i	−0.678060	+	0.391478i
$717$	−4.85294	−	33.4282i	−0.181236	−	1.24840i
$718$	7.30213	−	12.6477i	0.272513	−	0.472006i
$719$	17.8697	+	30.9513i	0.666429	+	1.15429i	0.978896	+	0.204360i	$0.0655114\pi$
$719$	17.8697	+	30.9513i	0.666429	+	1.15429i	−0.312467	+	0.949929i	$0.601155\pi$
$720$		0			0
$721$	11.0041	+	17.4166i	0.409813	+	0.648629i
$722$			8.07187i			0.300404i
$723$	−15.8681	−	6.32744i	−0.590139	−	0.235320i
$724$	15.2777	+	8.82061i	0.567793	+	0.327815i
$725$		0			0
$726$	41.7262	+	16.6385i	1.54861	+	0.617512i
$727$			33.2693i			1.23389i	0.787006	+	0.616945i	$0.211630\pi$
$727$			33.2693i			1.23389i	−0.787006	+	0.616945i	$0.788370\pi$
$728$	1.14326	+	28.6487i	0.0423722	+	1.06179i
$729$	17.5132	−	20.5497i	0.648636	−	0.761099i
$730$		0			0
$731$	9.15648	−	15.8595i	0.338665	−	0.586584i
$732$	3.87800	+	26.7127i	0.143335	+	0.987328i
$733$	14.5521	−	8.40163i	0.537492	−	0.310321i	−0.206570	−	0.978432i	$-0.566230\pi$
$733$	14.5521	−	8.40163i	0.537492	−	0.310321i	0.744062	+	0.668111i	$0.232897\pi$
$734$	−15.5158			−0.572700
$735$		0			0
$736$	−37.6414			−1.38748
$737$	−16.9404	+	9.78057i	−0.624009	+	0.360272i
$738$	12.1637	−	12.8270i	0.447753	−	0.472170i
$739$	−18.4120	+	31.8906i	−0.677297	+	1.17311i	0.298494	+	0.954411i	$0.403516\pi$
$739$	−18.4120	+	31.8906i	−0.677297	+	1.17311i	−0.975792	+	0.218702i	$0.929818\pi$
$740$		0			0
$741$	21.3895	+	27.1225i	0.785763	+	0.996371i
$742$	−0.137001	−	3.43305i	−0.00502945	−	0.126031i
$743$		−	45.3970i		−	1.66545i	−0.553684	−	0.832727i	$-0.686779\pi$
$743$		−	45.3970i		−	1.66545i	0.553684	−	0.832727i	$-0.313221\pi$
$744$	−0.744534	+	1.86716i	−0.0272959	+	0.0684532i
$745$		0			0
$746$	−9.62558	−	5.55733i	−0.352417	−	0.203468i
$747$	24.5524	−	7.28226i	0.898326	−	0.266444i
$748$			28.3060i			1.03497i
$749$	7.71466	+	12.2103i	0.281888	+	0.446156i
$750$		0			0
$751$	−9.49215	−	16.4409i	−0.346374	−	0.599937i	0.639229	−	0.769017i	$-0.279254\pi$
$751$	−9.49215	−	16.4409i	−0.346374	−	0.599937i	−0.985602	+	0.169080i	$0.945920\pi$
$752$	0.208057	−	0.360366i	0.00758707	−	0.0131412i
$753$	−45.5020	+	6.60575i	−1.65819	+	0.240727i
$754$	−9.01888	+	5.20705i	−0.328448	+	0.189630i
$755$		0			0
$756$	16.3054	+	0.835742i	0.593021	+	0.0303956i
$757$	24.7352			0.899017			0.449508	−	0.893276i	$-0.351599\pi$
$757$	24.7352			0.899017			0.449508	+	0.893276i	$0.351599\pi$
$758$	2.79116	−	1.61148i	0.101379	−	0.0585315i
$759$	73.2787	−	10.6382i	2.65985	−	0.386143i
$760$		0			0
$761$	23.8401	+	41.2923i	0.864204	+	1.49685i	0.867835	+	0.496852i	$0.165511\pi$
$761$	23.8401	+	41.2923i	0.864204	+	1.49685i	−0.00363106	+	0.999993i	$0.501156\pi$
$762$	−1.29104	+	1.01814i	−0.0467693	+	0.0368835i
$763$	15.4273	+	8.10457i	0.558505	+	0.293405i
$764$		−	22.1986i		−	0.803116i
$765$		0			0
$766$	−18.0554	−	10.4243i	−0.652368	−	0.376645i
$767$	−10.4674	−	6.04333i	−0.377954	−	0.218212i
$768$	−10.5618	+	26.4871i	−0.381117	+	0.955772i
$769$			48.8811i			1.76270i	0.472467	+	0.881349i	$0.343364\pi$
$769$			48.8811i			1.76270i	−0.472467	+	0.881349i	$0.656636\pi$
$770$		0			0
$771$	16.4417	+	20.8485i	0.592133	+	0.750842i
$772$	−1.54124	−	2.66950i	−0.0554704	−	0.0960775i
$773$	5.51932	−	9.55974i	0.198516	−	0.343840i	−0.749531	−	0.661969i	$-0.769721\pi$
$773$	5.51932	−	9.55974i	0.198516	−	0.343840i	0.948047	+	0.318129i	$0.103054\pi$
$774$	−9.01586	+	9.50751i	−0.324068	+	0.341740i
$775$		0			0
$776$	26.1611			0.939128
$777$	−4.65244	+	3.97995i	−0.166905	+	0.142780i
$778$	−15.3169			−0.549136
$779$	29.9347	−	17.2828i	1.07252	−	0.619221i
$780$		0			0
$781$	−6.98662	+	12.1012i	−0.250001	+	0.433015i
$782$	−11.5453	−	19.9971i	−0.412860	−	0.715095i
$783$	6.67161	+	14.4515i	0.238424	+	0.516456i
$784$	−0.851624	−	1.23586i	−0.0304152	−	0.0441379i
$785$		0			0
$786$	−15.1642	−	6.04677i	−0.540889	−	0.215681i
$787$	−14.6934	−	8.48325i	−0.523764	−	0.302395i	0.214709	−	0.976678i	$-0.431120\pi$
$787$	−14.6934	−	8.48325i	−0.523764	−	0.302395i	−0.738473	+	0.674283i	$0.764453\pi$
$788$	−8.05925	−	4.65301i	−0.287099	−	0.165757i
$789$	35.3784	+	14.1072i	1.25950	+	0.502231i
$790$		0			0
$791$	0.566649	−	0.0226129i	0.0201477	−	0.000804022i
$792$	12.6711	−	52.8616i	0.450246	−	1.87836i
$793$	−24.7479	−	42.8645i	−0.878822	−	1.52216i
$794$	−9.77475	+	16.9304i	−0.346893	+	0.600836i
$795$		0			0
$796$	−3.64492	+	2.10440i	−0.129191	+	0.0745884i
$797$	−11.9116			−0.421930			−0.210965	−	0.977494i	$-0.567661\pi$
$797$	−11.9116			−0.421930			−0.210965	+	0.977494i	$0.567661\pi$
$798$	−20.5919	−	7.27360i	−0.728946	−	0.257483i
$799$	−7.33457			−0.259478
$800$		0			0
$801$	−2.57210	−	2.43909i	−0.0908808	−	0.0861812i
$802$	0.221283	−	0.383274i	0.00781378	−	0.0135339i
$803$	7.94217	+	13.7562i	0.280273	+	0.485447i
$804$	3.95073	+	5.00965i	0.139332	+	0.176677i
$805$		0			0
$806$		−	1.37325i		−	0.0483708i
$807$	−19.1685	+	48.0712i	−0.674764	+	1.69218i
$808$	−5.73479	−	3.31098i	−0.201749	−	0.116480i
$809$	−8.58544	−	4.95680i	−0.301848	−	0.174272i	0.341425	−	0.939909i	$-0.389091\pi$
$809$	−8.58544	−	4.95680i	−0.301848	−	0.174272i	−0.643273	+	0.765637i	$0.722424\pi$
$810$		0			0
$811$		−	40.3504i		−	1.41689i	−0.705765	−	0.708446i	$-0.749396\pi$
$811$		−	40.3504i		−	1.41689i	0.705765	−	0.708446i	$-0.250604\pi$
$812$	−4.47633	+	8.52082i	−0.157088	+	0.299022i
$813$	16.8681	−	13.3026i	0.591590	−	0.466543i
$814$	3.79732	+	6.57715i	0.133096	+	0.230529i
$815$		0			0
$816$	−1.38894	+	0.201639i	−0.0486227	+	0.00705879i
$817$	−22.1879	+	12.8102i	−0.776255	+	0.448171i
$818$	−25.2768			−0.883783
$819$	−28.3398	+	9.65077i	−0.990273	+	0.337225i
$820$		0			0
$821$	21.2757	−	12.2835i	0.742527	−	0.428698i	−0.0804605	−	0.996758i	$-0.525639\pi$
$821$	21.2757	−	12.2835i	0.742527	−	0.428698i	0.822987	+	0.568060i	$0.192306\pi$
$822$	−11.2688	+	1.63595i	−0.393045	+	0.0570603i
$823$	−16.6942	+	28.9152i	−0.581924	+	1.00792i	0.413327	+	0.910583i	$0.364367\pi$
$823$	−16.6942	+	28.9152i	−0.581924	+	1.00792i	−0.995251	+	0.0973396i	$0.968967\pi$
$824$	−11.1859	−	19.3746i	−0.389680	−	0.674946i
$825$		0			0
$826$	7.63560	−	0.304709i	0.265677	−	0.0106022i
$827$		−	35.0677i		−	1.21942i	−0.792623	−	0.609712i	$-0.791285\pi$
$827$		−	35.0677i		−	1.21942i	0.792623	−	0.609712i	$-0.208715\pi$
$828$	−6.86750	−	23.1540i	−0.238662	−	0.804658i
$829$	−20.7299	−	11.9684i	−0.719979	−	0.415680i	0.0947660	−	0.995500i	$-0.469790\pi$
$829$	−20.7299	−	11.9684i	−0.719979	−	0.415680i	−0.814745	+	0.579820i	$0.803123\pi$
$830$		0			0
$831$	5.17605	−	12.9806i	0.179555	−	0.450291i
$832$		−	20.4956i		−	0.710555i
$833$	−11.3597	+	23.8917i	−0.393590	+	0.827800i
$834$	10.4936	+	13.3061i	0.363362	+	0.460754i
$835$		0			0
$836$	19.8004	−	34.2954i	0.684813	−	1.18613i
$837$	−2.09021	−	0.190938i	−0.0722484	−	0.00659980i
$838$	2.68638	−	1.55098i	0.0927994	−	0.0535778i
$839$	44.6267			1.54068			0.770342	−	0.637631i	$-0.220086\pi$
$839$	44.6267			1.54068			0.770342	+	0.637631i	$0.220086\pi$
$840$		0			0
$841$	19.6164			0.676428
$842$	−14.6720	+	8.47088i	−0.505631	+	0.291926i
$843$	−4.39784	−	30.2934i	−0.151470	−	1.04336i
$844$	−14.2358	+	24.6572i	−0.490018	+	0.848736i
$845$		0			0
$846$	5.10320	+	1.22325i	0.175452	+	0.0420562i
$847$	−64.3601	+	40.6636i	−2.21144	+	1.39722i
$848$			0.308914i			0.0106081i
$849$	−38.0877	−	15.1876i	−1.30717	−	0.521237i
$850$		0			0
$851$	7.84323	+	4.52829i	0.268863	+	0.155228i
$852$	4.23335	+	1.68806i	0.145032	+	0.0578320i
$853$			1.24909i			0.0427680i	0.999771	+	0.0213840i	$0.00680726\pi$
$853$			1.24909i			0.0427680i	−0.999771	+	0.0213840i	$0.993193\pi$
$854$	27.7030	+	14.5535i	0.947979	+	0.498011i
$855$		0			0
$856$	−7.84216	−	13.5830i	−0.268040	−	0.464258i
$857$	−4.60678	+	7.97918i	−0.157365	+	0.272564i	−0.933918	−	0.357488i	$-0.883633\pi$
$857$	−4.60678	+	7.97918i	−0.157365	+	0.272564i	0.776553	+	0.630052i	$0.216966\pi$
$858$	5.33534	+	36.7511i	0.182145	+	1.25466i
$859$	0.860775	−	0.496969i	0.0293693	−	0.0169564i	−0.485243	−	0.874379i	$-0.661269\pi$
$859$	0.860775	−	0.496969i	0.0293693	−	0.0169564i	0.514613	+	0.857423i	$0.327936\pi$
$860$		0			0
$861$	5.48287	+	29.4525i	0.186856	+	1.00374i
$862$	6.19664			0.211058
$863$	3.54799	−	2.04843i	0.120775	−	0.0697295i	−0.438395	−	0.898782i	$-0.644453\pi$
$863$	3.54799	−	2.04843i	0.120775	−	0.0697295i	0.559170	+	0.829053i	$0.311120\pi$
$864$	−28.7342	−	2.62483i	−0.977557	−	0.0892986i
$865$		0			0
$866$	6.88508	+	11.9253i	0.233965	+	0.405239i
$867$	−2.91430	−	3.69542i	−0.0989749	−	0.125503i
$868$	−0.677927	−	1.07299i	−0.0230104	−	0.0364195i
$869$		−	38.5919i		−	1.30914i
$870$		0			0
$871$	−10.1315	−	5.84944i	−0.343294	−	0.198201i
$872$	−16.3886	−	9.46197i	−0.554989	−	0.320423i
$873$	7.76768	+	26.1890i	0.262896	+	0.886364i
$874$			32.3045i			1.09272i
$875$		0			0
$876$	4.06801	−	3.20813i	0.137445	−	0.108393i
$877$	5.03871	+	8.72731i	0.170145	+	0.294700i	0.938471	−	0.345359i	$-0.112243\pi$
$877$	5.03871	+	8.72731i	0.170145	+	0.294700i	−0.768325	+	0.640060i	$0.778910\pi$
$878$	−17.3479	+	30.0474i	−0.585463	+	1.01405i
$879$	4.64180	−	0.673872i	0.156564	−	0.0227291i
$880$		0			0
$881$	30.3645			1.02301			0.511503	−	0.859281i	$-0.329089\pi$
$881$	30.3645			1.02301			0.511503	+	0.859281i	$0.329089\pi$
$882$	11.8884	−	14.7287i	0.400304	−	0.495941i
$883$	−16.1748			−0.544326			−0.272163	−	0.962251i	$-0.587739\pi$
$883$	−16.1748			−0.544326			−0.272163	+	0.962251i	$0.587739\pi$
$884$	−14.6609	+	8.46445i	−0.493098	+	0.284690i
$885$		0			0
$886$	−1.73803	+	3.01036i	−0.0583903	+	0.101135i
$887$	2.29479	+	3.97469i	0.0770514	+	0.133457i	0.901977	−	0.431785i	$-0.142116\pi$
$887$	2.29479	+	3.97469i	0.0770514	+	0.133457i	−0.824925	+	0.565242i	$0.808783\pi$
$888$	5.22052	−	4.11703i	0.175189	−	0.138159i
$889$	−0.111110	−	2.78428i	−0.00372652	−	0.0933816i
$890$		0			0
$891$	56.6803	−	3.01095i	1.89886	−	0.100871i
$892$	−17.4205	−	10.0577i	−0.583283	−	0.336758i
$893$	8.88652	+	5.13064i	0.297376	+	0.171690i
$894$	1.70034	−	4.26413i	0.0568678	−	0.142614i
$895$		0			0
$896$	−8.77326	−	13.8858i	−0.293094	−	0.463893i
$897$	27.4228	+	34.7729i	0.915620	+	1.16103i
$898$	−1.13639	−	1.96829i	−0.0379220	−	0.0656827i
$899$	0.618683	−	1.07159i	0.0206342	−	0.0357395i
$900$		0			0
$901$	4.71552	−	2.72251i	0.157097	−	0.0906998i
$902$	37.1619			1.23736
$903$	−4.06395	−	21.8305i	−0.135240	−	0.726473i
$904$	−0.615829			−0.0204822
$905$		0			0
$906$	1.11830	+	7.70310i	0.0371529	+	0.255918i
$907$	15.6580	−	27.1205i	0.519916	−	0.900521i	−0.479816	−	0.877369i	$-0.659297\pi$
$907$	15.6580	−	27.1205i	0.519916	−	0.900521i	0.999732	−	0.0231520i	$-0.00737016\pi$
$908$	−13.0026	−	22.5211i	−0.431505	−	0.747389i
$909$	1.61176	−	6.72400i	0.0534586	−	0.223021i
$910$		0			0
$911$			2.78118i			0.0921447i	0.998938	+	0.0460724i	$0.0146705\pi$
$911$			2.78118i			0.0921447i	−0.998938	+	0.0460724i	$0.985330\pi$
$912$	1.82388	+	0.727279i	0.0603948	+	0.0240826i
$913$	46.6245	+	26.9187i	1.54305	+	0.890878i
$914$	7.26289	+	4.19323i	0.240235	+	0.138700i
$915$		0			0
$916$		−	0.299327i		−	0.00989003i
$917$	23.3898	−	14.7780i	0.772400	−	0.488012i
$918$	−7.41887	−	16.0702i	−0.244859	−	0.530396i
$919$	−29.0225	−	50.2685i	−0.957365	−	1.65821i	−0.728860	−	0.684663i	$-0.759949\pi$
$919$	−29.0225	−	50.2685i	−0.957365	−	1.65821i	−0.228506	−	0.973543i	$-0.573384\pi$
$920$		0			0
$921$	1.36761	+	9.42046i	0.0450644	+	0.310415i
$922$	−8.89063	+	5.13301i	−0.292797	+	0.169047i
$923$	−8.35695			−0.275072
$924$	22.3115	+	26.0815i	0.733994	+	0.858018i
$925$		0			0
$926$	−0.251595	+	0.145259i	−0.00826793	+	0.00477349i
$927$	16.0740	−	16.9505i	0.527939	−	0.556728i
$928$	8.50504	−	14.7312i	0.279191	−	0.483574i
$929$	−20.7329	−	35.9104i	−0.680224	−	1.17818i	−0.974912	−	0.222589i	$-0.928549\pi$
$929$	−20.7329	−	35.9104i	−0.680224	−	1.17818i	0.294689	−	0.955593i	$-0.404784\pi$
$930$		0			0
$931$	30.4760	−	21.0008i	0.998809	−	0.688274i
$932$			17.7455i			0.581274i
$933$	−14.0157	+	35.1488i	−0.458853	+	1.15072i
$934$	−18.1993	−	10.5074i	−0.595499	−	0.343812i
$935$		0			0
$936$	31.1683	−	9.24454i	1.01877	−	0.302167i
$937$			15.3201i			0.500486i	0.968183	+	0.250243i	$0.0805105\pi$
$937$			15.3201i			0.500486i	−0.968183	+	0.250243i	$0.919489\pi$
$938$	7.39063	−	0.294933i	0.241312	−	0.00962990i
$939$	33.4442	−	26.3749i	1.09141	−	0.860714i
$940$		0			0
$941$	−25.5592	+	44.2698i	−0.833206	+	1.44316i	0.0622769	+	0.998059i	$0.480164\pi$
$941$	−25.5592	+	44.2698i	−0.833206	+	1.44316i	−0.895483	+	0.445096i	$0.853170\pi$
$942$	−10.9680	+	1.59227i	−0.357356	+	0.0518790i
$943$	38.3783	−	22.1577i	1.24977	−	0.721555i
$944$	−0.687068			−0.0223622
$945$		0			0
$946$	−27.5447			−0.895556
$947$	6.95988	−	4.01829i	0.226166	−	0.130577i	−0.382636	−	0.923899i	$-0.624984\pi$
$947$	6.95988	−	4.01829i	0.226166	−	0.130577i	0.608802	+	0.793322i	$0.291650\pi$
$948$	−12.4565	+	1.80837i	−0.404568	+	0.0587331i
$949$	−4.74996	+	8.22716i	−0.154190	+	0.267065i
$950$		0			0
$951$	−32.5794	+	25.6929i	−1.05646	+	0.833149i
$952$	13.3605	−	25.4321i	0.433017	−	0.824260i
$953$		−	43.7448i		−	1.41703i	−0.705695	−	0.708516i	$-0.749365\pi$
$953$		−	43.7448i		−	1.41703i	0.705695	−	0.708516i	$-0.250635\pi$
$954$	−3.73499	+	1.10780i	−0.120925	+	0.0358664i
$955$		0			0
$956$	−20.0578	−	11.5804i	−0.648714	−	0.374535i
$957$	−12.3939	+	31.0817i	−0.400639	+	1.00473i
$958$			0.570645i			0.0184367i
$959$	8.97489	−	17.0840i	0.289814	−	0.551670i
$960$		0			0
$961$	−15.4184	−	26.7055i	−0.497368	−	0.861467i
$962$	−2.27105	+	3.93358i	−0.0732217	+	0.126824i
$963$	11.2691	−	11.8836i	0.363140	−	0.382943i
$964$	−10.1439	+	5.85660i	−0.326714	+	0.188628i
$965$		0			0
$966$	−26.4002	−	9.32525i	−0.849413	−	0.300035i
$967$	−28.3067			−0.910281			−0.455140	−	0.890420i	$-0.650411\pi$
$967$	−28.3067			−0.910281			−0.455140	+	0.890420i	$0.650411\pi$
$968$	71.5954	−	41.3357i	2.30116	−	1.32858i
$969$	−4.97237	−	34.2509i	−0.159735	−	1.10030i
$970$		0			0
$971$	16.4304	+	28.4583i	0.527277	+	0.913270i	0.999495	+	0.0317882i	$0.0101202\pi$
$971$	16.4304	+	28.4583i	0.527277	+	0.913270i	−0.472218	+	0.881482i	$0.656546\pi$
$972$	−3.62783	−	18.1539i	−0.116363	−	0.582287i
$973$	−28.6963	+	1.14516i	−0.919961	+	0.0367123i
$974$			19.5144i			0.625282i
$975$		0			0
$976$	−2.43664	−	1.40680i	−0.0779950	−	0.0450304i
$977$	−44.2178	−	25.5291i	−1.41465	−	0.816750i	−0.418830	−	0.908065i	$-0.637560\pi$
$977$	−44.2178	−	25.5291i	−1.41465	−	0.816750i	−0.995822	+	0.0913150i	$0.970893\pi$
$978$	25.6452	+	10.2261i	0.820044	+	0.326995i
$979$		−	7.45178i		−	0.238160i
$980$		0			0
$981$	4.60601	−	19.2155i	0.147059	−	0.613505i
$982$	16.2965	+	28.2263i	0.520041	+	0.900737i
$983$	−15.0732	+	26.1076i	−0.480762	+	0.832704i	−0.999756	−	0.0220736i	$-0.992973\pi$
$983$	−15.0732	+	26.1076i	−0.480762	+	0.832704i	0.518994	+	0.854778i	$0.326307\pi$
$984$	−4.67394	−	32.1952i	−0.149000	−	1.02635i
$985$		0			0
$986$	10.4346			0.332306
$987$	−6.75816	+	5.78129i	−0.215115	+	0.184021i
$988$	23.6840			0.753489
$989$	−28.4463	+	16.4235i	−0.904541	+	0.522237i
$990$		0			0
$991$	−25.9382	+	44.9263i	−0.823955	+	1.42713i	0.0787606	+	0.996894i	$0.474904\pi$
$991$	−25.9382	+	44.9263i	−0.823955	+	1.42713i	−0.902715	+	0.430238i	$0.858430\pi$
$992$	1.12151	+	1.94252i	0.0356081	+	0.0616751i
$993$	29.0683	+	36.8595i	0.922456	+	1.16970i
$994$	4.46675	−	2.82215i	0.141677	−	0.0895133i
$995$		0			0
$996$	6.50390	−	16.3106i	0.206084	−	0.516821i
$997$	43.8884	+	25.3390i	1.38996	+	0.802494i	0.993310	−	0.115477i	$-0.0368395\pi$
$997$	43.8884	+	25.3390i	1.38996	+	0.802494i	0.396649	+	0.917970i	$0.370173\pi$
$998$	−7.03574	−	4.06209i	−0.222713	−	0.128583i
$999$	5.67149	+	4.00368i	0.179438	+	0.126671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.t.h.101.4	yes	20
3.2	odd	2	inner	525.2.t.h.101.7	yes	20
5.2	odd	4		525.2.q.g.374.7		40
5.3	odd	4		525.2.q.g.374.14		40
5.4	even	2		525.2.t.i.101.7	yes	20
7.5	odd	6	inner	525.2.t.h.26.7	yes	20
15.2	even	4		525.2.q.g.374.13		40
15.8	even	4		525.2.q.g.374.8		40
15.14	odd	2		525.2.t.i.101.4	yes	20
21.5	even	6	inner	525.2.t.h.26.4	✓	20
35.12	even	12		525.2.q.g.299.8		40
35.19	odd	6		525.2.t.i.26.4	yes	20
35.33	even	12		525.2.q.g.299.13		40
105.47	odd	12		525.2.q.g.299.14		40
105.68	odd	12		525.2.q.g.299.7		40
105.89	even	6		525.2.t.i.26.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.q.g.299.7		40	105.68	odd	12
525.2.q.g.299.8		40	35.12	even	12
525.2.q.g.299.13		40	35.33	even	12
525.2.q.g.299.14		40	105.47	odd	12
525.2.q.g.374.7		40	5.2	odd	4
525.2.q.g.374.8		40	15.8	even	4
525.2.q.g.374.13		40	15.2	even	4
525.2.q.g.374.14		40	5.3	odd	4
525.2.t.h.26.4	✓	20	21.5	even	6	inner
525.2.t.h.26.7	yes	20	7.5	odd	6	inner
525.2.t.h.101.4	yes	20	1.1	even	1	trivial
525.2.t.h.101.7	yes	20	3.2	odd	2	inner
525.2.t.i.26.4	yes	20	35.19	odd	6
525.2.t.i.26.7	yes	20	105.89	even	6
525.2.t.i.101.4	yes	20	15.14	odd	2
525.2.t.i.101.7	yes	20	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.780577 + 0.450666i) q^{2} +(-1.71408 + 0.248842i) q^{3} +(-0.593800 + 1.02849i) q^{4} +(1.22583 - 0.966719i) q^{6} +(0.105498 + 2.64365i) q^{7} -2.87309i q^{8} +(2.87616 - 0.853070i) q^{9} +O(q^{10})\)	\(q+(-0.780577 + 0.450666i) q^{2} +(-1.71408 + 0.248842i) q^{3} +(-0.593800 + 1.02849i) q^{4} +(1.22583 - 0.966719i) q^{6} +(0.105498 + 2.64365i) q^{7} -2.87309i q^{8} +(2.87616 - 0.853070i) q^{9} +(5.46176 + 3.15335i) q^{11} +(0.761890 - 1.91068i) q^{12} +3.77183i q^{13} +(-1.27375 - 2.01603i) q^{14} +(0.107205 + 0.185685i) q^{16} +(1.88963 - 3.27294i) q^{17} +(-1.86061 + 1.96207i) q^{18} +(-4.57893 + 2.64365i) q^{19} +(-0.838682 - 4.50518i) q^{21} -5.68443 q^{22} +(-5.87050 + 3.38933i) q^{23} +(0.714944 + 4.92471i) q^{24} +(-1.69984 - 2.94420i) q^{26} +(-4.71769 + 2.17794i) q^{27} +(-2.78161 - 1.46129i) q^{28} -3.06327i q^{29} +(0.349819 + 0.201968i) q^{31} +(4.80897 + 2.77646i) q^{32} +(-10.1466 - 4.04598i) q^{33} +3.40637i q^{34} +(-0.830485 + 3.46465i) q^{36} +(-0.668021 - 1.15705i) q^{37} +(2.38281 - 4.12714i) q^{38} +(-0.938588 - 6.46523i) q^{39} -6.53749 q^{41} +(2.68499 + 3.13867i) q^{42} +4.84564 q^{43} +(-6.48638 + 3.74491i) q^{44} +(3.05492 - 5.29127i) q^{46} +(-0.970371 - 1.68073i) q^{47} +(-0.229964 - 0.291602i) q^{48} +(-6.97774 + 0.557800i) q^{49} +(-2.42454 + 6.08030i) q^{51} +(-3.87929 - 2.23971i) q^{52} +(1.24774 + 0.720381i) q^{53} +(2.70100 - 3.82615i) q^{54} +(7.59543 - 0.303106i) q^{56} +(7.19082 - 5.67086i) q^{57} +(1.38051 + 2.39112i) q^{58} +(-1.60223 + 2.77514i) q^{59} +(-11.3644 + 6.56124i) q^{61} -0.364081 q^{62} +(2.55864 + 7.51354i) q^{63} -5.43385 q^{64} +(9.74358 - 1.41452i) q^{66} +(-1.55082 + 2.68611i) q^{67} +(2.24412 + 3.88694i) q^{68} +(9.21911 - 7.27042i) q^{69} +2.21562i q^{71} +(-2.45094 - 8.26345i) q^{72} +(2.18121 + 1.25932i) q^{73} +(1.04288 + 0.602109i) q^{74} -6.27919i q^{76} +(-7.76013 + 14.7716i) q^{77} +(3.64630 + 4.62362i) q^{78} +(-3.05960 - 5.29938i) q^{79} +(7.54454 - 4.90712i) q^{81} +(5.10301 - 2.94623i) q^{82} +8.53654 q^{83} +(5.13154 + 1.81259i) q^{84} +(-3.78240 + 2.18377i) q^{86} +(0.762268 + 5.25069i) q^{87} +(9.05984 - 15.6921i) q^{88} +(-0.590783 - 1.02327i) q^{89} +(-9.97138 + 0.397921i) q^{91} -8.05034i q^{92} +(-0.649878 - 0.259141i) q^{93} +(1.51490 + 0.874627i) q^{94} +(-8.93387 - 3.56241i) q^{96} +9.10556i q^{97} +(5.19528 - 3.58004i) q^{98} +(18.3989 + 4.41026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{3} + 14 q^{4} - 7 q^{9}+O(q^{10}) \) 20 * q - 3 * q^3 + 14 * q^4 - 7 * q^9	\( 20 q - 3 q^{3} + 14 q^{4} - 7 q^{9} + 21 q^{12} - 18 q^{16} - 14 q^{18} - 9 q^{21} - 20 q^{22} + 18 q^{24} + 10 q^{28} + 42 q^{31} - 12 q^{33} - 36 q^{36} - 24 q^{37} - 33 q^{42} - 36 q^{43} - 8 q^{46} - 4 q^{49} + 21 q^{51} + 84 q^{52} - 75 q^{54} - 6 q^{57} + 4 q^{58} - 90 q^{61} + 5 q^{63} - 120 q^{64} + 6 q^{66} - 20 q^{67} + 35 q^{72} + 48 q^{73} + 108 q^{78} + 46 q^{79} + 29 q^{81} - 36 q^{82} + 75 q^{84} - 69 q^{87} - 4 q^{88} - 30 q^{91} + 30 q^{93} + 6 q^{94} + 135 q^{96} + 94 q^{99}+O(q^{100}) \) 20 * q - 3 * q^3 + 14 * q^4 - 7 * q^9 + 21 * q^12 - 18 * q^16 - 14 * q^18 - 9 * q^21 - 20 * q^22 + 18 * q^24 + 10 * q^28 + 42 * q^31 - 12 * q^33 - 36 * q^36 - 24 * q^37 - 33 * q^42 - 36 * q^43 - 8 * q^46 - 4 * q^49 + 21 * q^51 + 84 * q^52 - 75 * q^54 - 6 * q^57 + 4 * q^58 - 90 * q^61 + 5 * q^63 - 120 * q^64 + 6 * q^66 - 20 * q^67 + 35 * q^72 + 48 * q^73 + 108 * q^78 + 46 * q^79 + 29 * q^81 - 36 * q^82 + 75 * q^84 - 69 * q^87 - 4 * q^88 - 30 * q^91 + 30 * q^93 + 6 * q^94 + 135 * q^96 + 94 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more